Exactly as it is because it has no mathematical signs to show whether or not it is to be added or multiplied
11 = (42 - 4) - (4 / 4) 12 = (4 + 4) + (√4 + √4) 13 = (42 - 4) + (4 / 4) 14 = (4 + 4 + 4 + √4) 15 = (4 * 4) - (4 / 4) 16 = (4 + 4 + 4 + 4) 17 = (42 + √4) - (4 / 4) 18 = (42 + 4) - (4 - √4) 19 = (42 + 4) - (4 / 4) 20 = (4 * 4) + (√4 + √4)
Here is one set of solutions. The answers here are not unique. 1 = (4*4)/(4*4) 2 = 4/4 + 4/4 3 = (4+4+4)/4 4 = (4-4)*4 + 4 5 = (4*4 + 4) / 4 6 = 4 + (4+4)/4 7 = 4 + 4 - 4/4 8 = 4 + 4 + 4 - 4 9 = 4 + 4 + 4/4 10 = (44 - 4)/4
3 simple solutions (there are more): (4-4)/4 + 4 = 4 4*(4-4)+ 4 = 4 4-((4-4)/4)) = 4
I'll start it, but I'm not going to finish it! 4 X 4 / 4 - 4 = 0 44 / 44 = 1 4 / 4 + 4 / 4 = 2 (4 + 4 + 4) / 4 = 3 (4 / 4)4 X 4 = 4 (4 / 4)4 + 4 = 5 (4 + 4) / 4 + 4 = 6 44 / 4 - 4 = 7 4 + 4 + 4 - 4 = 8 4 / 4 + 4 + 4 = 9 (44 - 4) / 4 = 10 (44 + 4) / 4 = 12 4! - 44 / 4 = 13 4! / 4 + 4 + 4 = 14 44 / 4 + 4 = 15 4 + 4 + 4 + 4 = 16 4 X 4 + 4 / 4 = 17 4 / √4 + 4 * 4 = 18 4! - 4 + 4 - 4 = 20 4! / 4 + 4 X 4 = 22 4 X 4 + 4 + 4 = 24 44 - 4 * 4 = 28 (4 + 4 / 4)! / 4 = 30 44 / (4 + 4) = 32 4! + 44 / 4 = 35 4! X 4! / 4 / 4 = 36 44 - 4 / √4 = 42 44 - 4 / 4 = 43 44(4/4) = 44 4 / 4 + 44 = 45 44 + 4 / √4 = 46 (4 + 4 + 4) X 4 = 48 √4 * 4 + 44 = 52 4 X 4 X 4 - 4 = 60 44 / 4 - √4 = 62 4(4 - 4/4) = 64 44 / 4 + √4 = 66 4 X 4 X 4 + 4 = 68 4! X 4! / (4 + 4) = 72 (4 X 4 + 4) X 4 = 80 (4 - 4 / 4)4 = 81 √4 * 44 - 4 = 84 √4 * 44 - √4 = 86 44 + 44 = 88 √4 * 44 + √4 = 90 √4 * 44 + 4 = 92 4! X 4 / 4 X 4 = 96
4/4 + 4/4 = 2 (one) 4 - (4+4)/4 = 2 (two) (4*4)/(4+4) = 2 (three) 4*(4/(4+4)) = 2 (four) ((4+4)/4) mod 4 = 2 (five) 4 + √4 - √4 - √4 = 2 (six) ((√4)/(√4)) + ((√4)/(√4)) = 2 (seven) 4 + 4 - 4 - √4 = 2 (eight) (√4)^4 / (4+4) = 2 (nine) (√(4*4)) / (4+4) = 2 (ten)
1 2 3 4 4+1 4+2 4+3 4+4 4+4+1 4+4+2 4+4+3 4+4+4 4+4+4+1 4+4+4+2 4+4+4+3 4+4+4+4 4+4+4+4+1 4+4+4+4+2 4+4+4+4+3 4+4+4+4+4 4+4+4+4+4+1 4+4+4+4+4+2 4+4+4+4+4+3 4+4+4+4+4+4 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+4+4+4+1 4+4+4+4+4+4+4+2 4+4+4+4+4+4+4+3 4+4+4+4+4+4+4+4 4+4+4+4+4+4+4+4+1 4+4+4+4+4+4+4+4+2 4+4+4+4+4+4+4+4+3 4+4+4+4+4+4+4+4+4 4+4+4+4+4+4+4+4+4+1 4+4+4+4+4+4+4+4+4+2 4+4+4+4+4+4+4+4+4+3 4+4+4+4+4+4+4+4+4+4 4+4+4+4+4+4+4+4+4+4+1 4+4+4+4+4+4+4+4+4+4+2 4+4+4+4+4+4+4+4+4+4+3 4+4+4+4+4+4+4+4+4+4+4 4+4+4+4+4+4+4+4+4+4+4+1 4+4+4+4+4+4+4+4+4+4+4+2 4+4+4+4+4+4+4+4+4+4+4+3 4+4+4+4+4+4+4+4+4+4+4+4 4+4+4+4+4+4+4+4+4+4+4+4+1 4+4+4+4+4+4+4+4+4+4+4+4+2 I hope this is the answer you search for! (because it took some time!)
26
1 = 4*4/(4*4) 2 = 4/4+4/4 3 = (4+4+4)/4 4 = (4-4)/4+4 5 = 4^(4-4)+4 6 = (4+4)/4+4 7 = 4+4-4/4 8 = 4+4+4-4 9 = 4/4+4+4 10 = (4*4+4!)/4 11 = (4+4!)/4+4 12 = (4-4/4)*4 13 = (4+4!+4!)/4 14 = 4!/4+4+4 15 = 4*4-4/4 16 = 4*4+4-4 17 = 4*4+4/4 18 = (4*4!-4!)/4 19 = 4!-(4+4/4) 20 = (4/4+4)*4 21 = 4!+4/4-4 22 = 4!-(4+4)/4 23 = 4!-4^(4-4) 24 = 4*4+4+4 25 = 4!+(4/4)^4 26 = 4!+4!/4-4 27 = 4!+4-4/4 28 = (4+4)*4-4 29 = 4/4+4!+4 30 = (4*4!+4!)/4 31 = (4+4!)/4+4! 32 = 4^4/(4+4) 33 = (4-.4)/.4+4! 34 = 4!/4+4+4! 35 = (4.4/.4)+4! 36 = (4+4)*4+4 37 = 4/.4+4+4! 38 = 44-4!/4 39 = (4*4-.4)/.4 40 = (4^4/4)-4! 41 = (4*4+.4)/.4 42 = 4!+4!-4!/4 43 = 44-4/4 44 = 4*4+4+4! 45 = (4!/4)!/(4*4) 46 = (4!-4)/.4 - 4 47 = 4!+4!-4/4 48 = (4*4-4)*4 49 = 4!+4!+4/4 50 = (4*4+4)/.4 51 = 4!/.4-4/.4 52 = 44+4+4 53 = 44+4/.4 54 = (4!/4)^4/4! 55 = (4!-.4)/.4-4 56 = 4!+4!+4+4 57 = 4/.4+4!+4! 58 = (4^4-4!)/4 59 = 4!/.4-4/4 60 = 4*4*4-4 61 = 4!/.4+4/4 62 = (4!+.4+.4)/.4 63 = (4^4-4)/4 64 = 4^(4-4/4) 65 = 4^4+4/4 66 = (4+4!)/.4-4 67 = (4+4!)/.4+4 68 = 4*4*4+4 69 = (4+4!-.4)/.4 70 = (4^4+4!)/4 71 = (4!+4.4)/.4 72 = (4-4/4)*4! 73 = (.4√4+.4)/.4 74 = (4+4!)/.4+4 75 = (4!/4+4!)/.4 76 = (4!-4)*4-4 77 = (4!-.4)/.4+4! 78 = (4!*.4+4!)/.4 79 = (.4√4-.4)/.4 80 = (4*4+4)*4 81 = (4/4-4)^4 82 = 4!/.4+4!+4 83 = (4!-.4)/.4+4! 84 = (4!-4)*4+4 85 = (4/.4+4!)/.4 86 = (4-.4)*4!-.4 87 = 4!*4-4/.4 88 = 4^4/4+4! 89 90 = (4!/4)!/(4+4) 91 92 = (4!-4/4)*4 93 94 = (4+4!)/.4 + 4! 95 = 4!*4-4/4 96 = 4!*4+4-4 97 = 4!*4+4/4 98 = (4!+.4)*4+.4 99 = (4!+4!-4)/.4 100 = 4*4/(.4*.4)
(4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4) ÷ 4 = 27
4 +4+4+4+4+4+4+4+4=40
Sure, using the number 4 four times, you can create the numbers 1 to 20 as follows: 1 = 4 / 4 + 4 - 4 2 = 4 / 4 + 4 / 4 3 = 4 - 4 / 4 + 4 4 = 4 + 4 - 4 - 4 5 = 4 + 4 / 4 6 = 4 + 4 - 4 / 4 7 = 4 + 4 / 4 + 4 8 = 4 + 4 + 4 / 4 9 = (4 + 4) / (4 / 4) 10 = 4 + 4 + 4 - 4 11 = 4 + 4 + 4 / 4 12 = 4 + 4 + 4 + 4 13 = (4 + 4) / 4 + 4 14 = 4 * 4 - 4 / 4 15 = 4 + 4 + 4 + 4 - 4 16 = 4 * 4 - 4 + 4 17 = 4 * 4 + 4 / 4 18 = (4 + 4) * (4 - 4) 19 = 4 * 4 + 4 - 4 20 = 4 * 4 + 4 / 4
The primes required are: 2 = (4+4)/4 3 = (4+4+4)/4 5 = (4+4+4+4+4)/4 7 = (4*4+4+4+4)/4 11 = (4(4*4-4)-4)/4 13 = (4*(4*4-4)+4)/4 17 = (4*4*4+4)/4 19 = (4*(4*4+4)-4)/4 23 = (4*(4*4+4+4)-4)/4 29 = (4*(4*4+4+4+4)+4)/4 31 = (4*4*(4+4)-4)/4 37 = (4*4*(4+4)+4*4+4)/4 41 = (4^4-4*(4*4)+4)/4 43 = (4^4-4(4*4+4+4))/4 47 = (4^4-4*4*4-4)/4 The remainder are left as an exercise. It should be noted that most of these are impossible to express with only six fours without either defining new operators or allowing for facetious, unmathematical cheats such as allowing 44 to be used.
1 = 44 / 442 = 4 * 4 / (4 + 4)3 = (4 + 4 + 4) / 44 = 4 + (4 * (4 - 4))5 = (4 + (4 * 4)) / 46 = 4 + ((4 + 4) / 4)7 = (44 / 4) - 48 = 4 + 4 + 4 - 49 = 4 + 4 + (4 / 4)10 = (44 - 4) / 411 = (4 / 4) + (4 / .4)12 = (4 + 44) / 413 = 4 + ((4 - .4) / .4)14 = (4 * (4 - .4)) - .415 = 4 + (44 / 4)16 = (44 - 4) * .417 = (4 * 4) + (4 / 4)18 = (44 * .4) + .419 = (4 + 4 - .4) / .420 = 4 * (4 + (4 / 4))
(4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4) / 4 = 17
4 4 4 44 4 4 4 44 4 4 4 44 4 4 4 4 4 4 4 4 34 4 4 4
0 = 44-44 1 = 44/44 or (4+4)/(4+4) or (4/4) / (4/4) 2 = 4/4+4/4 3 = (4+4+4)/4 4 = 4*(4-4)+4 5 = (4*4+4)/4 6 = 4*.4+4.4 7 = 44/4-4 8 = 4+4.4-.4 9 = 4/4+4+4 10 = 44/4.4 11 = 4/.4+4/4 12 = (44+4)/4 13 = 4-44/4 14 = 4*(4-.4)-.4 15 = 44/4+4 16 = .4*(44-4) 17 = 4/4+4*4 18 = 44*.4+.4 19 = 4!-4-4/4 20 = 4*(4/4+4) 21 = (4.4+4)/.4 22 = 44*sqrt(4)/4 23 = (4*4!-4)/4 24 = 4*4+4+4 25 = (4*4!+4)/4 26 = 4/.4+4*4 27 = 4-4/4+4! 28 = 44-4*4 29 = 4/.4/.4+4 30 = (4+4+4)/.4 31 = (4!+4)/4+4! 32 = 4*4+4*4 33 = (4+4! 34 = 44-4/.4 -6736 = 44-4-4 37 = (sqrt(4)+4!)/holy(4)+4! 38 = 44-4!/4 799740 = 44-sqrt(4*4) 42 = sqrt(4)+44-4 43 = 44-4/4 797945 = 4/4+44 46 = 44-sqrt(4)+4 47 = 4!+4!-4/4 48 = 4*(4+4+4) 49 = (4!-4.4)/.4 50 = 4!/4+44 52= (4!*4)-44 58= (sqrt(4)*(4!+4))+sqrt(4) 72= (4!*4)-4!*4o (small zero uptop four to the zero power = 1)
√4 × √4 + 4 - 4 = 4 √4 × √4 × 4/4 = 4