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 |
December 2018 - Math Problem
This triangle has 4 dots on each side. A total of 9 dots were used to make the triangle.
The bottom triangle has 6 dots on each side. A total of 15 dots were used to make the triangle.
November 2018 - Math Problem
A game played with coins has the following rules.
1. Coins are set up in a triangle.
2. Coins are moved until the triangle is upside down.
3. The number of moves is recorded.
For example, if a two-layer triangle is used, then only one move is required to flip the triangle.
October 2018 - Math Problem
If there were 8 people at a party and everyone shook everyone else's hand exactly once, how many handshakes would there be in total?
September 2018 - Math Problem
You throw a dart at the board below repeatedly. Each time you hit the board, you add either 7 or 3 to your score depending on which part you hit. What is the largest score that you can not get in this game? How do you know?
Solution:
Score 3 Hits 3