How Close To 100 Math Problem - Solution Requires Creativity

Hi there. Here is a math problem I would like to share. This is from my Mathnasium work where one of the students had a math homework problem which required a bit of creativity in developing a solution.

 

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The Close To 100 Problem

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If the text in the image is confusing here is my summary:

• Use each number once from 1, 2, 3, 4 all the way to nine.

• All the basic operations being +, -, x and ÷ have to be used when making 100 from the numbers one to nine. These operations can be used as many times as you like. (I would use each at least once.)

• Numbers can be combined in a way to create larger numbers. The number 123 can be constructed from using 1, 2 and 3. This counts as using the numbers 1, 2, 3 from to number list of 1 to 9 (inclusive).

• Although the question does not state it outright, order of operations (BEDMAS) does apply.

 

It Takes Trial & Error Until The Answer Is Right

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Mathematics is one of those subjects where it takes a lot of trial and error to get correct answers. It does take time and patience. Once the correct answer is found, there is a sigh of relief.

You could use a strategy where all the numbers used are single digit numbers and play with different combinations of numbers and operations to obtain one hundred. Remember that order of operations apply here. The problem does not mention about the use of brackets, fractions or exponents. Assume that you cannot do so.

One way is to start with a small number and increase your way to 100. Another way is to go from a big number down to 100. Addition and multiplication would be used to increase the total while subtraction and division would be used to decrease the total.

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One Solution

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Here is one answer to this problem that I have come up with.

I started with the number 96 from the digits 9 and 4. With 96, I divide this by 4. This gives me a quotient answer of 24. I then multiply by 5 to obtain 120. So far I have:

96 ÷ 4 x 5

Next I subtract 37 (random number when I was doing this). This uses up the 3 and 7 which leaves us with the digits 8, 2 and 1. This updated total is 120 - 37 = 83.

96 ÷ 4 x 5 - 37

From the number 83 I want to add by 17 to get 100. With the numbers 8, 2 and 1 remaining, I do 8 x 2 + 1. The final solution that I got is:

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Thank you for reading.