Four Fours is a wonderful mathematical puzzle with which I think everyone should be familiar. The goal of the game is create whole numbers using the following rules

- The expression must contain exactly four fours (and no other numbers)
- Any mathematical operation can be used
- The result must be a whole number
- The less operations used the better the solution

These rules are best illustrated with an example. “Create the number 0.”

Well, if you think about it for a bit (4 + 4) – (4 + 4) = 0. Tada! Here are some other neat solutions to get 0.

(4 ÷ 4) – (4 ÷ 4) = 0

(4 ÷ 4) * 4 – 4 = 0

44 – 44 = 0

You get the idea. How about “create the number 1.”

(4 ÷ 4) * (4 ÷ 4) = 1

Maybe 2 will be more challenging.

(4 ÷ 4) + (4 ÷ 4) = 2

Nope. Easy peasy lemon squeezy.

Now I could go ahead and post a long list of solutions for all the whole numbers up to 100, but that wouldn’t be very fun. I will post a couple of my favourites and let you fill in the rest on your own. Math is about creativity, having fun, and getting your hands dirty. I would hate to spoil this wonderful puzzle for you 🙂

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Here’s my answer to the first 30:

I assumed square roots to be “operations”, not powers of 1/2.

Otherwise, this is a bit harder, and I must revise a few.

0 = 44 – 44

1 = 44/44

2 = 4/4 + 4/4

3 = 4 – (4/4) mod 4 = 4 – 4^(4-4)

4 = 4*(4/4) mod 4 = 4*4^(4-4)

5 = 4 + (4/4) mod 4 = 5 = 4+4^(4-4)

6 = 4!/4*(4-4)

7 = 44/4-4

8 = (4+4) * 4/4 = 4*4-4-4

9 = 4+4+4/4

10 = (44-4)/4

11 = 44/sqrt(4*4)

12 = 4*4-4-4

13 = 44/4+sqrt(4)

14 = 4*4-4/sqrt(4)

15 = 4*4-4/4

16 = 4^4 / 4 / 4

17 = 4*4+4/4

18 = 4*sqrt(4)*sqrt(4) + sqrt(4)

19 = 4! – 4 – 4/4

20 = 4*(4+4/4)

21 = 4! – 4 + 4/4

22 = (4! – sqrt(4)) *4/4

23 = 4! – 4^(4-4)

24 = 4! * 4^(4-4)

25 = 4! + 4^(4-4)

26 = 4! +4/4*sqrt(4)

27 = 4! + 4 – 4/4

28 = 4! + 4*4/4

29 = 4! + 4 + 4/4

30 = (4+4+4)/.4