Make it True

Math Puzzles of the Month Make It True

See how many true mathematical sentences you can make out of a given collection of numbers. The idea for this puzzle came from 14-year-old Xiaoshuai.

We have four numbers: 1 2 3 4
Combine them into a true mathematical sentence whose answer is 5. For example:

4 + 3 - 2 x 1 = 5

Another true sentence with these same numbers is:

4 + 3 - 2 / 1 = 5

Can you come up with another true mathematical sentence with an arithmetic expression using 1, 2, 3, and 4 on the left side of the equation and 5 on the right side?

We are using the four standard arithmetic operations:

- subtract
x multiply
/ divide

The conventional order of operations applies: multiplication and division are done before addition and subtraction, and then, operations proceed from left to right. So, for example

3 + 4 x 2 = 11 (not 14) and
8 + 4 / 2 = 10 (not 6)

You may use parentheses to change this order. For example

(3 + 4) x 2 = 14
(8 + 4) / 2 = 6

Here’s another solution to our puzzle:

(4 + 1) / (3 - 2) = 5

There are more solutions. Try it for yourself.

More Puzzles

Here are some more puzzles to try. Insert arithmetic operations between the numbers on the left. You may use the same operation more than once. Use parentheses as you see fit. Some of these puzzles have only one solution. Others have more than one.

5 5 5 1 = 24
3 5 8 2 = 2
9 9 3 6 = 2
5 6 7 8 = 1
4 4 4 3 = 4
2 3 5 7 = 7