Question:

Find the Numbers 1-20 using Six Fours?

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So I have this math problem, find the numbers 1-20 with using all six Fours and any signs

EX : 4+4+4+4+4/4

It's exceedingly difficult, I would highly appreciate help.

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  1. 4/4 + 4/4 - 4/4 =  1

    4-4 + 4/4 + 4/4 = 2

    4/4 + 4/4 + 4/4 = 3

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

    (4*4)/(4*4) + 4 = 5

    4  +  4/4 + 4/4  = 6

    4+4+4 -4 - 4/4 = 7

    4 + 4 + 4/4 - 4/4 = 8

    4*4 - (4+4) + 4/4 = 9

    4 + 4 + 4/4 + 4/4 = 10

    I'm sure you can get the rest if you think about it.


  2. Got to kill some time so here goes.

    1 = (4 + 4 + 4)/(4 + 4 + 4)

    2 = (4 + 4 + 4)/4 - 4/4 or (4 + 4 + 4 + 4)/(4 + 4)

    3 = 4/4 + 4/4 + 4/4

    4 = (4 + 4)/4 + (4 + 4)/4

    5 = (4 + 4 + 4 + 4 + 4)/4

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

    7 = 4*(4 + 4)/4 - 4/4

    8 = 4 + (4 + 4 + 4 + 4)/4

    9 = 4 + 4 + (4 + 4)/(4 + 4) or (4 - 4/4)*(4 - 4/4)

    10 = 4 + 4 + 4/4 + 4/4

    11 = 4*(4 - 4/4) - 4/4

    12 = 4*(4 - 4/4) - 4 + 4

    13 = 4*(4 - 4/4) + 4/4

    14 = 4 + 4 + 4 + (4 + 4)/4

    15 = (4 + 4/4)*(4 - 4/4)

    16 = 4*(4 + 4 + 4 + 4)/4

    17 = 4*4 + (4 + 4)/(4 + 4)

    18 = 4*4 + 4/4 + 4/4

    19 = 4*4 + (4 + 4 + 4)/4

    20 = 4*(4 + (4 + 4)/4) - 4

  3. 1: 4-4+4-4+4/4

    2: 4-4+4/4+4/4

    3: 4/4+4/4+4/4

    4: (4+4)/4 + (4+4)/4

    5: 4+4-(4+4+4)/4

    6: 4+4-4/4-4/4

    7:4+4-4/4+4-4

    8: [(4+4)/4]*4 +4-4

    9: 4+4+4/4+4-4

    10: 4+4+4/4+4/4

    11:

    12:

    13:

    14: 4*4 -4/4 -4/4

    15: 4+4+4+4-4/4

    16: 4+4+4+4+4-4

    17: 4+4+4+4+4/4

    18: 4*4 -(4+4)/4 +4

    19: 4*4+(4+4+4)/4

    20: (4/4+4)*4+4-4

    That's about as far as I got before I needed to hit the hay.

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