February 2020 - Math Problem
What is the largest number of pieces of (round) pie that you can get with five straight cuts? The pieces do not all have to be the same size.
You have an unlimited supply of water and two unmarked cylindrical containers. The first container holds 5 litres and the other holds 3 litres. How would you get exactly 4 litres of water?
Solution:
Fill the five and pour what you can into the three
Empty the three and pour what remains in the five into the three.
January 2020 - Math Problem
You have a jar full of nickels, dimes and quarters. If you select 3 coins, how many different sums of money are possible?
Solution:
10 sums are possible (15, 20, 25, 30, 35, 40, 45, 55, 60 and 75). What if the jar also had loonies?
November 2019 - Math Problem
If there are three dots on each side of a hexagon as shown, then there are 12 dots in total.
If there are five dots on each side of a hexagon as shown, then there are 24 dots in total.
Following this pattern how many dots would there be in total if there were 10 dots on each side?
September 2019 - Math Problem
There are 50 tiles in a row. Every third tile is red. Every fourth tile has a star printed on it.
Every remaining tile is green and unmarked.
How many green and unmarked tiles are there?
There are 26 green and unmarked tiles. What if we started with 500 tiles instead of 50? How many would be green and unmarked?
Solution:
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June 2019 - Math Problem
Using all of the digits from 1 to 9 without repeating, make 3 three-digit numbers and add them up. How close to 1000 can you get without going over?
For example, one possibility would be 165+398+247=810.
Solution:
One way to get a sum of 999 is 537+168+294. Are there other ways to get a sum of 999? Is it possible to get a sum of 1000?
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May 2019 - Math Problem
Using the numbers 1, 3, 4 and 6, and the operations +, -, x, and / can you come up with the numbers from 1 to 20? You must use the numbers 1, 3, 4 and 6 exactly once in each calculation. You may use brackets as part of your work. For example:
1 = 4 x 1+ 3 - 6
2 = 4 + 3 - 6 + 1
3 = (6 + 3) / (4 - 1)
Solution:
1 = 4 x 1+ 3 - 6
2 = 4 + 3 - 6 + 1
3 = (6 + 3) / (4 - 1)
4 = (6 - 4) x (3 - 1)
5 = 4 x 3 - 6 - 1
6 = 6 - 4 +3 + 1
April 2019 - Math Problem
There are 10 closed lockers in a hallway and 10 students. The first student walks down the hallway and opens every locker. The second student walks down the hallway and closes every second locker. The third student walks down the hallway and closes every third open locker and opens every third closed locker. This process continues for all 10 students. How many lockers are open at the end?
Solution:
Three (3) lockers will be open at the end.
March 2019 - Math Problem
In this sequence of numbers (3, 7, 10, 17, 27), after the first two, each number is the sum of the previous two numbers. If you want the fifth number to equal 100, what two positive numbers could you start with?
Solution:
One possibility is 35 and 10 (35, 10, 45, 55, 100)
Another is 20 and 20 (20, 20, 40, 60, 100)
How many more can you come up with?
February 2019 - Math Problem
You have 4 different weights. The sum of the weights is 40 grams. If you have a two pan balance, you can use the 4 weights to make any weight from 1 gram to 40 grams. How many grams is each of the weights?
Solution:
The weights are 1 gram, 3 grams, 9 grams and 27 grams.
Following this pattern, how many grams would the next weight be? What range of weights could you make with these 5 weights?
January 2019 - Math Problem
You have 15 Loonies (one dollar coins) and four small bags. How many coins would you put into each bag so that you can pay any amount from $1 to $15 without opening bags?
Solution:
| Bag | Number of Coins |
|---|---|
| A | 1 |
| B | 2 |
| C | 4 |
| D | 8 |