2024 Year Challenge

arcsin⁡(20)/2+4!\arcsin(2^0)/2 + 4!

2024
2(0!+2)!+52^{(0!+2)! + 5}

2025

0=2+0−log⁡2(4)1=(2+0)⋅2/4=2/(0!/2)/42=2⋅0+log⁡2(4)3=(2+0!)!/log⁡2(4)4=2+0−2+45=(2+0!)2−46=20/2−47=2+0+2/.48=2+0!+2/.49=2+0!+2+4=(2+0!)log⁡2(4)=.2⋅sin⁡−1(0!)⋅2/410=(2+0!)⋅2+4=2⋅(0+2/.4)11=(2+0!)!+2/.412=2(0!+2)+413=(2+0!)2+414=20/2+415=20−2/.416=2/(0!/2)⋅417=20+2418=−(2⋅(0!+2))+4!=(2+0!)⋅(2+4)19=−2−0!−2+4!20=(2+0!+2)⋅4=((2+0!)!+2)/.421=20+2/422=20+2⋅423=−20+2424=(2+0!)⋅2⋅4=nPr(2+0!,2)⋅425=2/.02/4=20+2/.4=20/2/.426=2+0+2427=2+0!+2428=2+0+2+4!29=2+0!+2⋅4!30=(2+0!)⋅2+4!=(2+0!)!⋅2/.431=32=2(0!−2+4)=((2+0!)!+2)⋅4=nPr((2+0!)!,2)+433=.2⋅sin⁡−1(0!)/2+4!34=20/2+4!=nPr((2+0!)!,2)+435=36=20⋅2−4=(2+0!)2⋅4=(2+0!)!⋅(2+4)=2⋅sin⁡−1(0!)/(2/.4)37=38=(2+0!)!2+439=−2+sin⁡−1(0!)/2−440=20/2⋅441=sin⁡−1(20)/2−442=20−2+4!=(2+sin⁡−1(0!))/2−443=2+sin⁡−1(0!)/2−444=20⋅2+445=2⋅sin⁡−1(0!)/2/446=20+2+4!47=−2+sin⁡−1(0!)/2+448=(2+0!)!⋅2⋅449=20+2⋅4!=sin⁡−1(20)/2+450=(2+sin⁡−1(0!))/2+451=2+sin⁡−1(0!)/2+4=2+0!+2⋅4!60=(2+0+2)!/.4=2((2+0!)!)−4=.2⋅sin⁡−1(0!)⋅2+4!=nCr((2+0!)!,2)⋅4=(2+0!+2)!/461=62=−2+sin⁡−1(0!)−2463=64=2(0+2+4)=20⋅2+4!65=66=2+sin⁡−1(0!)−2467=−2+sin⁡−1(0!)/2+4!68=2((0!+2)!)+469=sin⁡−1(20)/2+4!70=(2+sin⁡−1(0!))/2+4!=−2⋅+sin⁡−1(0!)⋅2⋅.471=2+sin⁡−1(0!)/2+4!72=(2+0!)⋅24=−2+sin⁡−1(0!)−24=.2⋅sin⁡−1(0!)⋅2⋅4=nPr((2+0!)2,4)73=74=2+sin⁡−1(0!)⋅2⋅.475=76=2+sin⁡−1(0!)−2477=78=79=80=20⋅2⋅481=(2−0!+2)482=−2+sin⁡−1(0!)−2−4=2⋅(sin⁡−1(0!)/2−4)83=−2+sin⁡−1(0!)−2/.484=−2+sin⁡−1(0!)−2⋅485=sin⁡−1(20)−2/.486=2+sin⁡−1(0!)−2−487=2+sin⁡−1(0!)−2/.488=2+sin⁡−1(0!)−2−4=2((0!+2)!)+4!89=−2+sin⁡−1(0!)+2/490=.2⋅sin⁡−1(0!)⋅2/.4=(2+0!)!!/2/491=2+sin⁡−1(0!)−2/492=2+sin⁡−1(0!)−2+493=−2+sin⁡−1(0!)+2/.494=2+sin⁡−1(0!)+(2⋅4)95=nPr(20,2)/496=2/.02−4=(2+0!+2)!−4!97=2+sin⁡−1(0!)+2/.498=2+sin⁡−1(0!)+2+4=2⋅(sin⁡−1(0!)/2+4)=2⋅(0!+2⋅4!)99=100=20⋅2/.4=−20+(2/.4)!=202/4=−20+(2/.4)!egin{align*} \ 0 &= 2 + 0 - log_2(4) \ 1 &= (2 + 0) cdot 2 / 4 \ &= 2 / (0! / 2) / 4 \ 2 &= 2 cdot 0 + log_2(4) \ 3 &= (2 + 0!)! / log_2(4) \ 4 &= 2 + 0 - 2 + 4 \ 5 &= (2 + 0!)^2 - 4 \ 6 &= 20 / 2 - 4 \ 7 &= 2 + 0 + 2 / .4 \ 8 &= 2 + 0! + 2 / .4 \ 9 &= 2 + 0! + 2 + 4 \ &= (2 + 0!)^{log_2(4)} \ &= .2 cdot sin^{-1}(0!) cdot 2 / 4 \ 10 &= (2 + 0!) cdot 2 + 4 \ &= 2 cdot (0 + 2 / .4) \ 11 &= (2 + 0!)! + 2 / .4 \ 12 &= 2^(0! + 2) + 4 \ 13 &= (2 + 0!)^2 + 4 \ 14 &= 20 / 2 + 4 \ 15 &= 20 - 2 / .4 \ 16 &= 2 / (0! / 2) cdot 4 \ 17 &= 2^0 + 2^4 \ 18 &= -(2 cdot (0! + 2)) + 4! \ &= (2 + 0!) cdot (2 + 4) \ 19 &= -2 - 0! - 2 + 4! \ 20 &= (2 + 0! + 2) cdot 4 \ &= ((2 + 0!)! + 2) / .4 \ 21 &= 20 + 2 / sqrt{4} \ 22 &= 20 + sqrt{2 cdot sqrt{4}} \ 23 &= -2^0 + 24 \ 24 &= (2 + 0!) cdot 2 cdot 4 \ &= ext{nPr}(2 + 0!, 2) cdot 4 \ 25 &= 2 / .02 / 4 \ &= 20 + 2 / .4 \ &= 20 / 2 / .4 \ 26 &= 2 + 0 + 24 \ 27 &= 2 + 0! + 24 \ 28 &= 2 + 0 + 2 + 4! \ 29 &= 2 + 0! + 2 cdot 4! \ 30 &= (2 + 0!) cdot 2 + 4! \ &= (2 + 0!)! cdot 2 / .4 \ 31 &= \ 32 &= 2^(0! - 2 + 4) \ &= ((2 + 0!)! + 2) cdot 4 \ &= ext{nPr}((2 + 0!)!, 2) + sqrt{4} \ 33 &= .2 cdot sin^{-1}(0!) / 2 + 4! \ 34 &= 20 / 2 + 4! \ &= ext{nPr}((2 + 0!)!, 2) + 4 \ 35 &= \ 36 &= 20 cdot 2 - 4 \ &= (2 + 0!)^2 cdot 4 \ &= (2 + 0!)! cdot (2 + 4) \ &= 2 cdot sin^{-1}(0!) / (2 / .4) \ 37 &= \ 38 &= (2 + 0!)!^2 + sqrt{4} \ 39 &= -2 + sin^{-1}(0!) / 2 - 4 \ 40 &= 20 / 2 cdot 4 \ 41 &= sin^{-1}(2^0) / 2 - 4 \ 42 &= 20 - 2 + 4! \ &= (2 + sin^{-1}(0!)) / 2 - 4 \ 43 &= 2 + sin^{-1}(0!) / 2 - 4 \ 44 &= 20 cdot 2 + 4 \ 45 &= 2 cdot sin^{-1}(0!) / 2 / sqrt{4} \ 46 &= 20 + 2 + 4! \ 47 &= -2 + sin^{-1}(0!) / 2 + 4 \ 48 &= (2 + 0!)! cdot 2 cdot 4 \ 49 &= 2^0 + 2 cdot 4! \ &= sin^{-1}(2^0) / 2 + 4 \ 50 &= (2 + sin^{-1}(0!)) / 2 + 4 \ 51 &= 2 + sin^{-1}(0!) / 2 + 4 \ &= 2 + 0! + 2 cdot 4! \ 60 &= (2 + 0 + 2)! / .4 \ &= 2^((2 + 0!)!) - 4 \ &= .2 cdot sin^{-1}(0!) cdot 2 + 4! \ &= ext{nCr}((2 + 0!)!, 2) cdot 4 \ &= (2 + 0! + 2)! / sqrt{4} \ 61 &= \ 62 &= -2 + sin^{-1}(0!) - 24 \ 63 &= \ 64 &= 2^(0 + 2 + 4) \ &= 20 cdot 2 + 4! \ 65 &= \ 66 &= 2 + sin^{-1}(0!) - 24 \ 67 &= -2 + sin^{-1}(0!) / 2 + 4! \ 68 &= 2^((0! + 2)!) + 4 \ 69 &= sin^{-1}(2^0) / 2 + 4! \ 70 &= (2 + sin^{-1}(0!)) / 2 + 4! \ &= -2 cdot + sin^{-1}(0!) cdot 2 cdot .4 \ 71 &= 2 + sin^{-1}(0!) / 2 + 4! \ 72 &= (2 + 0!) cdot 24 \ &= -2 + sin^{-1}(0!) - 2^4 \ &= .2 cdot sin^{-1}(0!) cdot 2 cdot sqrt{4} \ &= ext{nPr}((2 + 0!)^2, sqrt{4}) \ 73 &= \ 74 &= 2 + sin^{-1}(0!) cdot 2 cdot .4 \ 75 &= \ 76 &= 2 + sin^{-1}(0!) - 2^4 \ 77 &= \ 78 &= \ 79 &= \ 80 &= 20 cdot 2 cdot sqrt{4} \ 81 &= (2 - 0! + 2)^4 \ 82 &= -2 + sin^{-1}(0!) - 2 - 4 \ &= 2 cdot (sin^{-1}(0!) / 2 - 4) \ 83 &= -2 + sin^{-1}(0!) - 2 / .4 \ 84 &= -2 + sin^{-1}(0!) - 2 cdot sqrt{4} \ 85 &= sin^{-1}(2^0) - 2 / .4 \ 86 &= 2 + sin^{-1}(0!) - 2 - 4 \ 87 &= 2 + sin^{-1}(0!) - 2 / .4 \ 88 &= 2 + sin^{-1}(0!) - 2 - sqrt{4} \ &= 2^((0! + 2)!) + 4! \ 89 &= -2 + sin^{-1}(0!) + 2 / sqrt{4} \ 90 &= .2 cdot sin^{-1}(0!) cdot 2 / .4 \ &= (2 + 0!)!! / 2 / 4 \ 91 &= 2 + sin^{-1}(0!) - 2 / sqrt{4} \ 92 &= 2 + sin^{-1}(0!) - 2 + sqrt{4} \ 93 &= -2 + sin^{-1}(0!) + 2 / .4 \ 94 &= 2 + sin^{-1}(0!) + sqrt(2 cdot sqrt{4}) \ 95 &= ext{nPr}(20, 2) / 4 \ 96 &= 2 / .02 - 4 \ &= (2 + 0! + 2)! - 4! \ 97 &= 2 + sin^{-1}(0!) + 2 / .4 \ 98 &= 2 + sin^{-1}(0!) + 2 + 4 \ &= 2 cdot (sin^{-1}(0!) / 2 + 4) \ &= 2 cdot (0! + 2 cdot 4!) \ 99 &= \ 100 &= 20 cdot 2 / .4 \ &= -20 + (2 / .4)! \ &= 20^2 / 4 \ &= -20 + (2 / .4)! end{align*}