Four Fours

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

  1. The expression must contain exactly four fours (and no other numbers)
  2. Any mathematical operation can be used
  3. The result must be a whole number
  4. 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 🙂

4*\cos{(4-4)}+4=8

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

\left( \lfloor \exp{(4)} \rfloor - \sqrt{4} - \sqrt{4} \right) * \sqrt{4} = 100

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1 Comment

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One response to “Four Fours

  1. Matias

    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

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