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)
Cities that have the same latitude as Miami, which is approximately 25.8 degrees north, include Riyadh in Saudi Arabia, Abu Dhabi in the United Arab Emirates, and Doha in Qatar. These cities are all located along the Tropic of Cancer, which is an imaginary line that circles the Earth parallel to the equator. They share similar climatic conditions due to their proximity to the tropics.
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)