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0 0 0 0 = 24

A fun puzzle that kept my friends and me up at night

Athena Xiao
4 min readSep 19, 2021

Game 24

Game 24 is a classic math game for grade school students. According to Wikipedia:

Game 24

Game 24 is an arithmetical card game in which the objective is to find a way to manipulate four integers so that the end result is 24.

For example, for the card with the numbers 4, 7, 8, 8, a possible solution is:

(8 / 8) = 1

7 - 1 = 6

6 * 4 = 24

I could still remember when I used to play Game 24 with myself using the numbers from license plates of cars on the street, while sitting on the back of my mom’s moped.

The classic approach is to break it down to 6 * 4 = 24, 8 * 3 = 24, or occasionally 12 * 2. The goal is to manipulate 4 numbers into the pair of (6, 4), (8, 3), or (12, 2).

Of course this approach doesn’t cover every case. For example,

8 9 3 1 = 24

8 * 9 = 72

72 / 3 = 24

24 * 1 = 24

You can tackle it from 72 / 3 = 24, 96 / 4 = 24, 21 + 3 = 24, 28 - 4 = 24 and many more! Try more examples here.

0 0 0 0 = 24?

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