## Problems, Answers and Solutions

Were you able solve the problems? We have posted the solutions to the problems and an explanation for each question.

If you are interested in exploring our after-school math classes for bright, gifted and high performing students in Grade 1- 11, use the location tool at right to search for a campus near you. You may also want to check out our upcoming Open Houses (where you can meet with teachers, ask questions, and review our curriculum.

**Question – Posted to Social Media on November 17, 2017**

**Q: **Joanna is going to wrap a present and she wants to know how much wrapping paper she will need. She knows that she needs to measure the box first, but which of the following measurements would be the best for her to figure out how much paper she must buy?

**Answer: **Joanna will need to know the surface area of the present.

#### Explanation

The wrapping paper will cover the surface area of the box, therefore surface area would be the best unit of measurement to know before purchasing the wrapping paper.

**Question – Posted to Social Media on November 10, 2017**

**Q: **At Emily’s party, eleven girls ate a total average of 3 pizzas. At Kai’s party, eight boys ate a total average of 5 pizzas. How many more pizzas in total would the girls at Emily’s party need to eat to average the same number of pizzas that the boys ate at Kai’s party?

**Answer: **The girls at Emily’s party should eat 22 more pizzas to average the same number as the boys at Kai’s party.

#### Explanation

For the girls to average 5 pizzas, they will have to eat 11 x 5 = 55 pizzas. They ate 3 x 11 = 33 pizzas, so they would need to eat another 55 – 33 = 22 pizzas more in total.

**Question – Posted to Social Media on November 3, 2017**

**Q:** A 405 inch long submarine sandwich is cut into 6 pieces. The second piece is one inch longer than the first piece. The third piece is one inch longer than the second piece. The fourth piece is one inch longer than the third piece. The fifth piece is one inch longer than the fourth piece. The sixth piece is one inch longer than the fifth piece. What is the length of the longest piece of sandwich?

**Answer:** The length of the longest piece is 70 cm.

#### Explanation

If the first piece is a length of n, then:

n + (n + 1) + (n + 2) + (n + 3) _ (n + 4) + (n + 5) = 405. This means that 6n + 15 = 405, or 6n = 390 and the first length is 65 cm. The last piece would be 65 + 5 = 70 cm.

**Question – Posted to Social Media on October 27, 2017**

**Q: **While trick-or-treating on Halloween night, Joanna collected 16 candies, Mary collected 18 candies and Kim collected 7 candies. If the average number of candies collected by Nathan, Marc and Andrew was 14, what group collected more candies, the boys or girls?

**Answer:** The boys collected more candy.

#### Explanation

The girls had 16 + 18 + 7 = 41 pieces of candy, while the boys had 14 x 3 = 42 pieces of candy.

**Question – Posted to Social Media on October 27, 2017**

**Q: **In a small village in Pakistan, the ratio between the number of boys and number of girls is 2 : 3, and the ration between the number of girls and number of toys is 8 : 1. What is the ratio between the numberof children (boys and girls) and number of toys?

**Answer:** 40 : 3

**Question – Posted to Social Media on October 20, 2017**

**Q: **Twenty children were chosen to each recite a poem on stage with one of the other children for the annual Diwali Celebration. If each child recited a poem with each of the other children, how many poems were read in all?

**Answer:** 190

#### Explanation

If you multiply 20 x 19, then you would count twice as many duets as were actually played. The number of duets that were actually played would be: 20 x 19 ÷ 2 = 190 duets.

This is the same as the sum of all the natural numbers from 1 to 19.

**Question – Posted to Social Media on October 20, 2017**

**Q: **A Spirit of Math student from City School Campus in Lahore is preparing for a math contest. She beings reading her workbook from the top of page 15 and ends on the bottom of page 27. How many pages did she read?

**Answer:** 13 pages

#### Explanation

If she read all pages up to and including page 27, she would have read 27 pages. But she didn’t read all the pages, she started at the top of page 15, so she didn’t read 14 pages. This means that she only read 27 – 14 = 13 pages.

Last page read – # of pages not read = # of pages read

27 – 14 = 13 pages read

**Question – Posted to Social Media on October 13, 2017**

**Q: **Spirit of Math students invented a new game called “Genius Ball” in which each team has three players. Coach Omar has seven players, two of those players are brothers who have brought only one pair of shoes and cannot both play at the same time. How many teams of three players can coach Omar create to play the game?

**Answer:** 30

#### Explanation

Melissa has bought 5¢ and 10¢ stamps for a total of 55¢. If she were to buy the same number of 5¢ stamps, but twice the number of 10¢ stamps, it would cost her $1.05. From these two premises, we can infer that the amount paid for the 10¢ stamps is (105¢ – 55¢) 50¢. The number of 10¢ stamps she has bought is (50¢ ÷10¢) 5 and that of 5¢ is ((55¢ – 50¢) ÷ 5¢) 1.

**Question – Posted to Social Media on October 6, 2017**

**Q:** Melissa has bought 5¢ and 10¢ stamps for a total of 55¢. If she were to buy the same number of 5¢ stamps, but twice the number of 10¢ stamps, it would cost her $1.05. How many 5¢ stamps did she buy?

**Answer:** 1

#### Explanation

Melissa has bought 5¢ and 10¢ stamps for a total of 55¢. If she were to buy the same number of 5¢ stamps, but twice the number of 10¢ stamps, it would cost her $1.05. From these two premises, we can infer that the amount paid for the 10¢ stamps is (105¢ – 55¢) 50¢. The number of 10¢ stamps she has bought is (50¢ ÷10¢) 5 and that of 5¢ is ((55¢ – 50¢) ÷ 5¢) 1.

**Question – Posted to Social Media on September 29, 2017**

**Q:** At the end of a hockey game between the Toronto Maple Leafs and the Ottawa Senators, each of the players on one team gave a handshake to each of the players on the other team. If there are 14 players on each team, how many handshakes were made in total by both teams at the end of the game?

**Answer:** 196

#### Explanation

**Solution:** Every player on the Maple Leafs would shake 14 players hands on the Senators team. There are 14 Maple Leafs shaking 14 Senators’ hands, or 14 x 14 = 196. This is different from many of the other questions because they are shaking hands with other people, not within the same team!

**Question – Posted to Social Media on September 22, 2017**

**Q:** Of the 75 children who registered in after-school courses, 14 registered in both math and science, 26 registered only in math, and 31 registered in science. How many of the 75 children did not register in either math or science?

**Answer:** There were 18 children who did not enrol in either math or science. (Common wrong answers: 4 and 32)

#### Explanation

**Solution:** Use a Venn diagram, filling in the numbers given in the question. It is important to realize that the statement “31 enrolled in science” doesn’t mean that 31 enrolled ** only** in science. The 31 includes the 14 who enrolled in both math and science, so you must subtract 31 – 14 = 17 to find the number who enrolled only in science. With the Venn diagram complete, you can calculate the answer to the problem. The answer is 75 – (26 + 14 + 17) = 18.

**Alternate Solution: **Ignore the 14, since it is already included in the 31 enrolled in pottery. This gives the calculation 75 – (26 + 31) = 18.

**Question – Posted to Social Media on September 15, 2017**

**Q:** A Grade 5 math class has an average of 19/40 on their drill scores and they want to get an average of 30/40. By how much would the 9 students have to increase their total score in order to achieve this?

**Answer:** The 9 students would have to increase their total score by 99 so they can achieve an average of 30/40.

#### Explanation

**Solution:** With a class average of 19/40, the class has a total score of: 19 x 9 = 171. If they want to increase their average to 30/40, then their total score needs to be: 30 ÷ 9 = 270.

The total score would have to increase by 270 – 171 = 99 marks.

**Alternate Solution: **For the overall average to increase by 11 marks, this would be the same as each student increasing their mark by 11 marks. There are 9 students, so the total score would be increased by 9 x 11 = 99 marks.

**Question – Posted to Social Media on September 8, 2017**

**Q:** What is the 200th number in the sequence 3, 7, 11, … ?

**Answer:** The 200th number is 799.

#### Explanation

**Solution:** The numbers increase by 4, so you just add multiples of 4. If the letters “n” is used to represent the number of terms, then the equation can be written as: 3 + (n – 1) x 4, where 3 is the first term and (n – 1) is the term before the one that you are trying to get.

The 3rd term is 3 + (3 – 1) x 4 = 3 + 8, or 11.

The 200th number is 3 + 199 x 4 = 799

**Question – Posted to Social Media on September 1, 2017**

**Q:** At the start of a trip, the odometer on Elvis’s motorcycle read 179,971 km. At the end of the trip, Elvis noticed that the odometer reading was the next palindromic number. What was the odometer reading at the end of the trip?

**Answer:** 180,081 km

**Question – Posted to Social Media on August 25, 2017**

**Q:** Several Spirit of Math students brought their bicycles and tricycles to their classes and parked them outside the building. If there were a total of 14 seats and 34 wheels, how many students brought their tricycles?

**Answer:** Six students brought tricycles.

#### Explanation

**Solution:** If all the wheels belonged to bicycles, then there would be 14 x 2 = 28 wheels. But there are 34 wheels, so the remaining 34 – 28 = 6 wheels go on each of the tricycles. There are 6 tricycles. The number of bicycles is not asked for here, so it doesn’t need to be calculated. If you are wondering, the number of bicycles is 14 – 6 = 8.

**Question – Posted to Social Media on August 18, 2017**

**Q:** The Mathland Symphony Orchestra has 25 musicians. Of these, 12 can play brass instruments, 8 can play violin and 10 can play the drums. There are 6 who can play both brass and violin, 5 who can play both violin and drums and 7 who can play both the drums and brass. in addition, 4 can play all 3 types of instruments. How many play none of these instruments?

**Answer:** Nine of the musicians play neither the brass, violin, or drums.

#### Explanation

**Solution:** To solve this Brain Boggler you’ll need to create a Venn Diagram. Start by placing the 4 in the middle of the diagram. Since 6 can play both brass and violin, this means that 2 play just the brass and violin. Place a 2 in the area over-lapped by the 2 circles. Continue this way until you have all the numbers in the areas where the 2 circle overlap. Then you can fill in the numbers that belong in only 1 circle. At the end add up all the numbers in the circles to get: 3 + 2 + 4 + 3 + 1 + 1 + 2 = 16. This means that 25 – 16 = 9.

**Question – Posted to Social Media on August 11, 2017**

**Q:** A watch loses 2 minutes every hour. If it now shows 7:45, what time was it displaying exactly 30 hours earlier?

**Answer:** Thirty hours earlier it was 2:45.

#### Explanation

**Solution:** In 1 hour, the clock loses 2 minutes. In 30 hours, it would lose 2 x 30 = 60 minutes. Therefore the time now should show 60 minutes later, or an hour after 7:45, which is 8:45. Thirty hours before 8:45 is exactly a day and 6 hours earlier, or 2:45.

**Question – Posted to Social Media on August 4, 2017**

**Q:** At the annual dog show there were people and dogs everywhere! Melissa counted the number of legs and the number of heads. If she counted 186 heads and 496 legs, how many dogs were at the show?

**Answer:** There are 62 dogs.

#### Explanation

**Solution: **If every head belonged to a person then there would be 186 x 2 = 372 legs. Melissa counted 496 legs, which is more than 372, so some of those “heads” belonged to dogs. There were 496 – 372 = 124 extra legs that belong to dogs. The extra legs would go on the dogs in pairs. There are 124 ÷ 2 = 62 extra pairs of legs. Therefore, there are 62 dogs.

**Question – Posted to Social Media on July 28, 2017 **

**Q:** Two trains are heading toward each other on a collision course on the same piece of straight track. One train travels at 62 km/h and the other at 85 km/h. If they start out 900 km apart, how far apart are they 1 hour before they meet?

**Answer:** The trains are 147 km apart one hour before they meet.

#### Explanation

**Solution: **Ignore the 900 km: it’s not important. Work backward from the crash. One hour before the trains meet, the first train is 62 km from the crash site (since it moves 62 km every hour) and the second train is 85 km away in the opposite direction. The distance between them is therefore: 62 km + 85 km = 147 km.

**Question – Posted to Social Media on July 21, 2017 **

**Q: **Bart, the ultimate prankster, decided to treat Homer to six days of pranks! He pulled 3 pranks the first day, 6 on the second day, 11 on the third day, 18 on the fourth day and 29 on the fifth day. If this pattern continues, how many pranks will he pull on the sixth day?

**Answer:** Bart will pull 42 pranks on the sixth day.

#### Explanation

**Solution: **The numbers in the pattern are 3, 6, 11, 18, 29. The difference between the first 2 numbers is 3, the difference between the second and third is 5, and the third and fourth is 7.

The pattern to calculate the next number is +3, +5, +7, +11, which are the prime numbers in order. The next prime is 13, so the next number in the sequence is 29 + 13 = 42.

**Question – Posted to Social Media on July 14, 2017 **

**Q: **Sailboat Sam leaves the yacht club travelling to Lagoon Island at 3.4 km per hour. At the same time, Paddleboat Polly leaves Lagoon Island for the yacht club, travelling at 5.6 km per hour. If the distance between the yacht club and Lagoon Island is 24.8 km, then how far apart are Sam and Polly one hour before they meet?

**Answer:** Sailboat Sam and Paddleboat Polly are 9 km apart one hour before they meet.

#### Explanation

**Solution: **The distance between the yacht club and Lagoon Island, 24.8 km, is not needed to solve this problem. What is needed is the sum of the distances each boat travels in one hour: 3.4 + 5.6 = 9 km, because that is the distance one hour before they meet.

**Question – Posted to Social Media on July 7, 2017 **

**Q: **Charlie just scored big at the chocolate factory! He won 15 chocolate bars that he wants to share with 5 of his friends. How many chocolate bars would Charlie give to each of his friends to ensure everyone gets their fair share?

**Answer:** Each friend would get 3 chocolate bars.

#### Explanation

**Solution: **Divide 15 by 5 friends. 15 ÷ 5 = 3 (Notice that this does not include “Charlie.”) This is the same as the average.

**Question – Posted to Social Media on June 30, 2017**

**Q: **Enroute to yet another gold medal, Team Canada played a hockey tournament against 5 other teams. There were 513 shots on net in the tournament’s 9 games. What was the average number of shots on net per game?

**Answer:** The average number of shots on net per game was 57.

#### Explanation

**Solution: **Total shots = 513

Number of games = 9

513 ÷ 9 = 57

**Question – Posted to Social Media on June 23, 2017**

Q: Daniel wanted to buy a skateboard, but all he needed was a little extra money – money he knew he would receive on his birthday. If Daniel’s birthday was 7 days before the day following November 1st, when will he have enough money to buy the skateboard he wants so badly?

**Answer: **Daniel will have enough money to buy the skateboard on November 6th.

#### Explanation

**Solution: **The anchor date is November 1. Starting with that date and working backwards to create an equation you will get: 1 + 1 – 3 +7 = 6. His birthday is on November 6th.

**Question – Posted to Social Media on May 19, 2017 **

Q: There are ten players on the Raptors basketball team. If each of them shook hands with each other once, how many handshakes were there?

**Answer: **45 handshakes

**Question – Posted to Social Media on May 12, 2017**

**Q: **Matt bought a new football for $10. He sold it to his friend for $5 more than he paid for it. His friend sold it to a store for $20. Did Matt’s friend make money or lose money? How much?

**Answer: **Matt’s friend made $5.

#### Explanation

**Solution: **If Matt sold the football to his friend for $5 more than what he paid for it, that means that his friend paid him $15 dollars for the football. His friend then sold the football for $20, which means he made a $5 profit on the football.

**Grade 3 Question – Posted to Social Media on April 28, 2017:**

**Q: **Four books are placed side-by-side on a table. The red book is not beside the blue or yellow book. The blue book is to the right of the green book. The yellow book is beside only one other book. What is the proper order of the books?

**Answer: **Red – Green – Blue – Yellow

#### Explanation

**Solution: **If the average of 5 numbers is 21, then the sum of those 5 numbers will be 21 x 5 = 105. Likewise, the sum of the 6 numbers will be 23 x 6 = 138. This means that the number included was 138 – 105 = 33.

**Grade 6 Question – Posted to Social Media on April 7, 2017:**

**Q:** A book is open up at random. The product of the page numbers is 7482. What are the page numbers?

**Answer:** 86 & 87

#### Explanation

Since facing page numbers are one apart, we can estimate. The value of 80 times 80 is 6400 and the value of 90 times 90 is 8100, so we know the pages must be in the 80’s because the product of the two pages we want, 7482, is between 6400 and 8100. In an open book, the right-hand page number is an odd number, so we try the combinations (80,81), (82,83), (84,85), (86,87), (88,89). Only the last two pairs give a product whose last digit is 2, so we try these.

**Grade 9 Question – Posted to Social Media on March 31, 2017**

**Q:** Twelve guests are to be seated for dinner. Six of them have already chosen to sit in a row at a bar table, and the other six will sit in a circle at a round table. What is the total number of different seating arrangements for these guests?

**Answer: **86400

#### Explanation

**Solution:** There are 6! = 720 ways to arrange the guests at the bar table. For each of these ways, there are 5! = 120 ways to arrange the six guests at the round table. (In a circular permutation, one person has to be placed first, and the others are arranged around that person.) The total number of arrangements is 720 x 120 = 86400.

**Grade 9 Question – Posted to Social Media on March 24, 2017:**

**Q:** Patty uses stickers with digits printed from 0 to 9 to number the pages of her scrapbook. She has lots of all digits except the digit 3, and she only has 37 of these. How many pages can she number in her scrapbook with this limitation?

**Answer: **172

#### Explanation

**Solution:** From 1 to 99 there are twenty 3s: ten in the unit’s places and ten in the ten’s places. From 100 to 123 there are 2 more 3s, making a total of 23. From 130 to 139 there are another eleven, for a total of 34. The 35th will be at 143, the 36th at 153, and the 37th at 163. From there, Patty can still number up to page 172 before she is stuck for lack of 3s.

**Grade 9 Question – Posted to Social Media on March 17, 2017:**

**Q:** A train takes 144 seconds from the time it enters a tunnel that is 1500 m long, until it is completely through the tunnel. A stationary ceiling light in the tunnel is directly above the train for 24 seconds. How long is the train (in metres)?

**Answer: **300 m

#### Explanation

**Solution:** It takes the train 24 seconds to completely enter the tunnel. It then stays completely in the tunnel for another 120 seconds, before it starts to leave the tunnel. The tunnel is therefore the length of five trains, and the train is therefore 1500 / 5 = 300 m long.

**Grade 9 Question – Posted to Social Media on March 10, 2017**

**Q:** A hockey team plays 85 games in a season. The team has won 12 games and lost 15 so far. What percentage of the remaining games must it win to achieve a 60% winning average for the year? (Round to the nearest tenth.)

**Answer: **67.2%

#### Explanation

**Solution:** The team has already played 12 + 15 = 27 games, and have 85 – 27 = 58 more games to play. To achieve a 60% win record, they must win a total of 0.6 x 85 = 51 games in total. They must win 51 – 12 = 39 of their remaining 58 games, for a percentage of 39/58 x100 = 67.2%

**Grade 3 Question – Posted to Social Media on March 3, 2017:**

**Q: **The average of 5 numbers is 21. When a sixth number is included, the new average is 23. What number was included?

**Answer: 33**

#### Explanation

**Solution: **Start with blue and green: blue goes to the right of green. Since red is not beside blue, it will go to the left of green. Yellow is only beside one other book, so it goes on the far right. This creates the order of red, green, blue, and yellow.

**Grade 6 Question – Posted to Social Media on Feb. 24, 2017:**

**Q:** In fifteen days it will be the first of the month. Fifteen days ago it was the first of the month. It is also summer time. Give today’s date (month and day).

**Answer:** September 16

#### Explanation

**Solution:** 16 – 15 = 1, and 16 + 15 = 31 (so the month must have 30 days). June 16 is still springtime, so the date must be September 16.

**Grade 7 Question – Posted to Social Media on Feb. 17, 2017:**

**Q:** There are six short pieces of chain, each with four links. If it costs 70¢ to cut a link and $1.65 to weld it back together, what is the least cost, in dollars, to make the longest possible chain?

**Answer: **$9.40

#### Explanation

**Solution:** If one of the short 4-link pieces of chain has each link broken, then these four links can be used to join together the 5 other pieces of chain. The total cost is (.70 + 1.65) × 4=$9.40

**Grade 4 Question – Posted to Social Media on Feb. 10, 2017:**

**Q: **Janet won the lottery! She kept half of the money for herself, gave $500 000 to her mother, half of what remained to her sister, half of what remained after that to her daughter, and the remaining $200 000 to a charity. How much did Janet win?

**Answer: **$2 600 000

#### Explanation

**Solution: **The daughter and the charity each received $200 000, which totals $400 000. So the sister received $400 000, making a total of $800 000 so far. Janet’s mother received $500 000, bringing the total to $1 300 000 for the giveaways. This is half of Janet’s money, so Janet won $2 600 000.

**Grade 3 Question – Posted to Social Media on: Feb. 3, 2017:**

**Q: **At the Crazy Frog Pond, all 30 frogs like to eat flies. Twenty-two of the frogs also like to eat crickets and 16 of the frogs also like to eat mice. How many frogs like flies, crickets and mice?

**Answer: **8

#### Explanation

**Solution: **If you add the number of frogs that like to eat crickets and the number of frogs that like to eat mice, you will get 22 + 16 = 38. However, there are only 30 frogs; these “extras” are the ones that like to eat crickets as well as mice. Therefore, 38 – 30 = 8 frogs eat flies, crickets, and mice.

**Grade 8 Question – Posted to Social Media on Jan. 27, 2017):**

**Q: **A bus driver who starts with a large empty bus picks us 11 riders at every odd-numbered stop and drops off 5 riders at every even-numbered stop. The stop after which the bus will first contain more than 165 passengers is stop number…?

**Answer: **53

#### Explanation

**Solution:** The stop is an odd-numbered stop, before which there were 154 or more passengers. Six extra riders are gained every two stops. Since 26×6 =156 , we go 52 stops to have 156 passengers, and on the 53rd stop there will be 167 passengers.

**Grade 6 Question – Posted to Social Media on Jan. 20, 2017:**

**Q:** Which is greater: a half dozen dozen pairs of cupcakes or a half of two dozen dozen cupcakes?

**Answer: **They’re the same

#### Explanation

**Solution:** Half a dozen dozen pairs is 6 × 12 × 2 = 144. Half of two dozen dozen is 0.5 × 24 × 12 = 144.

**Grade 3 Question – Posted to Social Media on Jan. 13, 2017:**

**Q: **Judy had her dance recital 6 days before 3 days after one week before her tooth fell out. If her tooth fell out on June 12, when was Judy’s dance recital?

**Answer: **June 2

#### Explanation

Start from the day Judy’s tooth fell out and work backwards: 12 – 7 + 3 – 6 = 2

**Grade 3 Question – Posted to Social Media on Jan. 6, 2017:**

**Q: **Sam has 6 striped socks, 4 polkadot socks, and 11 plain socks in his dresser drawer. How many socks must he take out in order to be sure of getting a pair of polkadot socks?

**Answer: **18

#### Explanation

Sam must take out all the striped, all the plain and 2 of the polkadot socks in order to be absolutely sure of getting a pair of polkadot socks.

**Grade 3 Question – Posted to Social Media on Dec. 30, 2016:**

**Q: **Zoe saw elves and reindeer at Santa’s workshop. She counted 242 legs and 73 heads. How many elves does Santa have?

**Answer: 25**

#### Explanation

Solution: Assume all were elves: each elf has 2 legs, so that would be a total of 73 x 2 = 146 legs. However, she saw 242 legs, so that’s 242 – 146 = 96 more legs, which belong to the reindeer. Since two more legs are needed for each reindeer, there are 96 ÷ 2 = 48 pairs of legs left over, which means there are 48 reindeer, and 73 – 48 = 25 elves at the workshop.

**Grade 4 Question – Posted to Social Media on Dec. 16, 2016:**

**Q: **Bobbie loves blowing bubbles. How many ways can she arrange the letters in the word BUBBLE, including the way that spells “bubble”?

**Answer: **120

#### Explanation

There are 6 letters in the word BUBBLE, with 3 Bs that repeat. The total number of arrangements is

**Grade 4 Question – Posted to Social Media on Dec. 09, 2016:**

**Q: **Silly mirrors at Franky’s Fun House are numbered consecutively from 38 to 64. Mirrors that make you shrink have odd numbers on them. Mirrors that make you stretch have even numbers on them. How many mirrors will make you shrink?

**Answer: **13

#### Explanation

Find the number of odd numbers between 38 and 64 to begin with: 64 – 37 (last number not used) = 27 numbers from 38 to 64. Divide by 2 to find the number of odd numbers: 27 / 2=13 remainder 1, which means there are 14 even numbers (since the sequence starts and ends with an even number) and 13 odd numbers. Therefore 13 mirrors will make you shrink.

**Grade 6 Question – Posted to Social Media on Dec. 2, 2016:**

**Q: **Stephen’s watch loses time. Stephen set his watch to the correct time at 10 am, but noticed three hours later that it read 12:54 pm. If Stephen does not adjust his watch, at what time according to his watch should he show up at the restaurant for a 7:00 pm date with Mabel?

**Answer: **6:42 pm

#### Explanation

Stephen’s watch loses 6 minutes in 3 hours, which is equivalent to 2 minutes an hour. From 10 AM to 7 PM is 9 hours, in which time the watch loses 9 x 2 = 18 minutes. Therefore Stephen must arrive 18 minutes before 7:00, or at 6:42 PM.

**Grade 7 Question – Posted to Social Media on Nov. 25, 2016:**

**Q: **A cube of ice, 160 cm to an edge and weighing 480 kg, is left sitting in the hot sun. After several hours it is still a cube, but measures 80 cm to an edge. How much weight has it lost?

**Answer: **420 kg

#### Explanation

Since the dimensions of the block after melting are half the original dimensions, the new volume is one eighth the original volume ( ). Now x 480 = 60, and 480 – 60 = 420 kg.

**Grade 6 Question – Posted to Social Media on Nov. 18, 2016):**

**Q: **Georges is watering her garden, which contains red, blue, and yellow flowers. If all the flowers are red except 14, and all are blue except 18, and all are yellow except 12, then how many flowers are in Georges’ garden?

**Answer: **22

#### Explanation

Blue + red = 14, red + yellow = 18, and blue + yellow = 12. Adding these, 14 + 18 + 12 = 44, but this counts each flower twice, so there are 44 / 2 = 22 flowers.

**Grade 2 Question – Posted to Social Media on Nov. 11, 2016:**

**Q: **At the grocery store, you can buy 3 lemons for 60¢. How much it cost to buy one dozen lemons?

**Answer: $2.40**

#### Explanation

**Solution:** There are 12 lemons in a dozen. Since 3 lemons x 4 = 12 lemons, multiply 60¢ by 4 to find the cost of a dozen lemons: 60 x 4 = 240 cents, which is $2.40.

**Grade 5 Question – Posted to Social Media on Nov. 4, 2016):**

**Q: **Peter and Karen are siblings. Peter has as many brothers as sisters. Karen has twice as many brothers as sisters. How many boys and how many girls are in the family?

**Answer: **4 boys and 3 girls

#### Explanation

**Solution: **Since Peter has as many brothers as sisters, the number of boys must be one more than the number of girls. The number of boys must also be an even number, since Karen has twice as many brothers as sisters. Two boys and 1 girl doesn’t work because there has to be more than 1 girl (aside from Karen). Four boys and 3 girls works: Karen has 2 sisters and four brothers, and Peter has 3 sisters and 3 brothers.

**Grade 6 Question – Posted to Social Media on Oct. 28, 2016:**

**Q:** A clock takes 12 seconds to strike 4. How long does it take to strike 12? ( Hint: it is not 36 seconds)

**Answer: **44 seconds

#### Explanation

Count the spaces *between* strikes! If the clock takes 12 seconds to strike 4, there are three 4-second intervals. To strike 12, it would use eleven 4-second intervals, which is 44 seconds.

**Grade 7 Question Posted to Social Media on Oct. 21, 2016:**

**Q:** In how many ways can 7 people be seated in a row of 9 chairs if Jane and Joe must sit next to each other?

**Answer: **40320

#### Explanation

Consider first the special case of Jane and Joe. Sitting next to each other, there are 8 different places they could take on the 9 chairs, and because they could sit with either Jane or Joe on the left, there are 16 different positions. Now there are 5 people and 7 chairs left. The number of ways to choose 5 chairs out of 7 is ways. So the next people to sit down have, in order, 5 choices of seats, then 4 choices, 3 choices 2 choices and 1 choice (5! = 120 ways). Multiplying, we have 16 x 21 x 120 = 40 320 different arrangements.

**Grade 2 Question – Posted to Social Media on Oct. 14,2016:**

**Q:**Eight girls went to a party and gave each other a hug. How many hugs did they give each other altogether?

**Answer: **28

#### Explanation

Each of the eight girls hugged seven other girls. Since two girls share a hug, divide by two to eliminate double-counting: 8 x 7 / 2 = 28.

**Grade 5 Question:**

**Q:** Peter and Karen are siblings. Peter has as many brothers as sisters. Karen has twice as many brothers as sisters. How many boys and how many girls are in the family?

**Answer: **4 boys and 3 girls

#### Explanation

Since Peter has as many brothers as sisters, the number of boys must be one more than the number of girls. The number of boys must also be an even number, since Karen has twice as many brothers as sisters. Two boys and 1 girl doesn’t work because there has to be more than 1 girl (aside from Karen). Four boys and 3 girls works: Karen has 2 sisters and four brothers, and Peter has 3 sisters and 3 brothers.

**Grade 7 Question:**

**Q:** Prove that the area of a triangle is equal to the radius of the inscribed circle of the triangle times the semi-perimeter of the triangle.

#### Explanation

**Solution:** Each of the sides of the triangle is tangent to the circumference of the circle. If you draw radii to the points of intersection of the triangle and circle (as shown below in magenta), then each of these radii will form a 90° angle with the sides of the triangle. If you draw line segments from the centre of the circle (O) to each of the vertices of the triangle (shown below in green), you now have 3 pairs of congruent triangles (VADO ≅ VAFO, VBDO ≅ VBEO, and VCEO ≅ VCFO). Looking, for instance, at VADO and VAFO, these two triangles are congruent because AD = AF (these two line segments are both tangent to the circle and share an endpoint). Likewise, the segments labelled *b* are equal and the segments labelled *c* are equal.

**Grade 9 Question:**

**Q:** A school with 60 teachers is on alert during a nighttime storm. To inform teachers whether the school will open the next day, the principal will call four teachers, each of whom will call two others, and each of these will call two others, and so on until all 60 teachers have been contacted. How many teachers will have to make 2 calls?

**Answer: **28

#### Explanation

**Solution:** Each of the four teachers must call two others, making 8 people who then need to call two others. The 16 people contacted must phone 32 others. At this point, 4 + 8 + 16 = 28 teachers have called two others. The other 32 have received calls, but do not need to phone anyone.