June 2024 - Neighbourhood Math Adventures
Welcome to the Math Trail! Get ready to explore your neighborhood and have fun while solving math problems.
Feel free to modify the trail based on the amount of time you have to explore! Have a fantastic time exploring and applying your mathematical reasoning skills in your neighborhood.
Stop 1: Street Signs Bingo
Problem of the Month - May 2024
Place the digits 0 to 8 in the grid above so that the sum of every row and every column is a multiple of 6.
Solution(s) will be posted at the end of the month
Problem of the Month - April 2024
How many rectangles (including squares) are there in this picture?
Solution(s)
There are 36 rectangles. (There are twelve 1 x 2 rectangles, six 1 x 3 rectangles, four 2 x 3 rectangles, nine 1 x 1 squares, four 2 x 2 squares, and one 3 x 3 square)
Problem of the Month - February 2024
When a number is multiplied by itself, the answer is a perfect square.
For example, 25 is a perfect square because 5 x 5 is 25.
In how many ways can the number 1764 be written as the product (multiply) of two perfect squares?
Solution
1764 can be written as a product of two perfect squares in three ways.
- 4 x 441
- 9 x 196
- 36 x 49
(It can also be written as a product of three perfect squares 4 x 9 x 49)
Problem of the Month - January 2024
In how many ways can 15 identical red blocks be put into four piles so that each pile has at least one block and no two piles have the same number of blocks?
(The order of the piles does not matter).
Solution(s)
There are 6 ways to create four piles with 15 objects and no piles have the same number of objects.
1 2 3 9
1 2 4 8
1 2 5 7
1 3 4 7
1 3 5 6
2 3 4 6
Problem of the Month - December 2023
Which is a better deal, one round pizza that is 18 inches in diameter for $15 or two round pizzas that are both 12 inches in diameter for $15?
Solution
The 18 inch diameter pizza is a better deal. The area of a circle can be found by the formula A=pi x radius x radius. The area of the top of the 18 inch diameter pizza is about 254 square inches. The area of the top of one 12 inch diameter pizza is about 113 square inches so two of them would have a top area of about 226 square inches.
Problem of the Month - November 2023
A person starts at 5 and counts by 10s, so they count 5, 15, 25, …
Another person starts at 700 and counts by 3s, so they count 700, 703, 706, …
If they start at the same time and say their numbers at the same rate, who will get over 1000 first?
Solution
The person counting by 10s will get over 1000 first. The person who is counting by 10s will be over 1000 after saying 101 numbers. The person who is counting by 3s will be at 1000 after saying 101 numbers and will be over 1000 after saying 102 numbers
Problem of the Month - October 2023
If you roll two six-sided fair dice are you more likely to get an even result if you add the top numbers or if you multiply them?
Solution
You are more likely to get an even result if you multiply the dice. If you add them the probability of getting an even number is ½. If you multiply the numbers, the probability of getting an even number is ¾.
Problem of the Month - September 2023
Seven points are randomly placed on the circle shown below.
How many different triangles can be drawn using these points as vertices?
Solution
Problem of the Month - June 2023
Suppose there was one of six prizes inside your favourite box of cereal.
How many boxes of cereal would you expect to have to buy to get all six prizes?
Simulate this with a six-sided die. Roll the die and keep track of how many rolls it takes to get all 6 numbers.
Repeat the experiment several times.
Approximate the answer to this question by finding the mean (arithmetic average) of all of your results