Math Problems

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(s) will be posted at the end of the month

Math Problems

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

 

 

Math Problems

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. 

Math Problems

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

Math Problems

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.

Math Problems

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

Math Problems

Problem of the Month - May 2023

Can you find four consecutive numbers which add up to 10? 

How about four consecutive numbers that add to 22?  How about 110? 

Solution

1+2+3+4=10; 4+5+6+7=22; 26+27+28+29=110. 

Can you find four consecutive numbers that add to 298?

Math Problems

Problem of the Month - March 2023

You are ordering round pizzas. 

If you want more pizza, would it make sense to order two 12 inch diameter pizzas or one 18 inch diameter pizza?

 

Solution

If you wanted more pizza, it would make sense to order one 18 inch pizza. 

What if you wanted more crust? 

Would it be better to order two 12 inch diameter pizzas or one 18 inch diameter pizza?

Math Problems