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Is there a way to express 100 by using the first four natural numbers in order?

The numbers 1, 2, 3, 4 can be linked by using $+$, $-$, $\times$, $\div$, $($ $)$, $!$ and exponents are also allowed. But you are not allowed to leave the integers.

Examples: $$-1+(2+3)^4=624$$ $$(1!+2)^{3^4}= large$$

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  • 2
    $\begingroup$ Brute force is likely applicable for this kind of problem, just list all possibilities using a computer... $\endgroup$
    – PC1
    Nov 17, 2021 at 17:17
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    $\begingroup$ Can you explain your first example? I evaluate the left hand side to be $624$. Also, what is the : operator? $\endgroup$
    – John Douma
    Nov 17, 2021 at 17:21
  • $\begingroup$ @PC1 you are absolutly right. $\endgroup$ Nov 17, 2021 at 17:23
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    $\begingroup$ Is concatenation accepted? That is, would $12+3^4=93$ be a valid expression? $\endgroup$
    – Glen O
    Nov 18, 2021 at 3:06
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    $\begingroup$ $(1+(-2+3!)!)\cdot 4=100$ $\endgroup$ Nov 18, 2021 at 6:53

1 Answer 1

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Seems more like a Puzzling.SE question to me but here's a CW post for others to edit. 79/100 complete

Number Expression
1 $-1+2\cdot3-4$
2 $1+2+3-4$
3 $1+2\cdot3-4$
4 $1+2-3+4$
5 $1^{2\cdot3}+4$
6 $1-2+3+4$
7 $-1+2\cdot3!-4$
8 $-1+2+3+4$
9 $1\cdot2+3+4$
10 $1+2+3+4$
11 $1-2+3\cdot4$
12 $1^2\cdot3\cdot4$
13 $1+2+3!+4$
14 $1\cdot(2+3\cdot4)$
15 $-(1+2)!-3+4!$
16 $-1\cdot2^3+4!$
17 $1-2^3+4!$
18 $-1\cdot2\cdot3+4!$
19 $-1 + (2+3)\cdot 4$
20 $(-1+2+3)!-4$
21 $-(1+2)!+3+4!$
22 $-(-1^2+3)!+4!$
23 $-(1^{2\cdot3})+4!$
24 $-1-2+3+4!$
25 $-(1\cdot2)+3+4!$
26 $1-2+3+4!$
27 $-1-2+3!+4!$
28 $-1+2+3+4!$
29 $1-2+3!+4!$
30 $1+2+3+4!$
31 $-1+2+3!+4!$
32 $1\cdot2^3+4!$
33 $1+2+3!+4!$
34
35 $-1+2!\cdot3!+4!$
36 $1\cdot2!\cdot3!+4!$
37 $1+2!\cdot3!+4!$
38
39 $-1+2^{3!}-4!$
40 $ (1+2)! \cdot 3! +4$
41 $1+2^{3!}-4!$
42 $(1+2)!\cdot(3+4)$
43 $1+2\cdot(-3+4!)$
44 $(-1+2\cdot3!)\cdot4$
45
46
47 $-1+2\cdot3!\cdot4$
48 $(1^2+3)!+4!$
49 $1+2\cdot3!\cdot4$
50
51 $(1+2)^3+4!$
52 $(1+2\cdot3!)\cdot4$
53 $-1+2\cdot(3+4!)$
54 $(1+2)!^3/4$
55 $1+2\cdot(3+4!)$
56
57
58
59 $-1+2^{3!}-4$
60 $(1+2)!\cdot3!+4!$
61 $1+2^{3!}-4$
62
63 $(1+2)\cdot(-3+4!)$
64
65
66
67 $-1+2^{3!}+4$
68 $1\cdot2^{3!}+4$
69 $1+2^{3!}+4$
70 $-1\cdot2+3\cdot4!$
71 $-1^2+3\cdot4!$
72 $1^2\cdot3\cdot4!$
73 $1^2+3\cdot4!$
74 $1\cdot2+3\cdot4!$
75 $-(1+2)!+3^4$
76
77
78 $-1-2+3^4$
79 $-(1\cdot2)+3^4$
80 $1-2+3^4$
81 $1^2\cdot3^4$
82 $-1+2+3^4$
83 $1\cdot2+3^4$
84 $1+2+3^4$
85
86
87 $-1+2^{3!}+4!$
88 $1\cdot(2^{3!}+4!)$
89 $1+2^{3!}+4!$
90 $(1+2)\cdot(3!)!/4!$
91
92 $(1-(-2+3!)!)\cdot(-4)$
93
94
95 $-1+(2+3)!-4!$
96 $1\cdot(2+3)!-4!$
97 $1+(2+3)!-4!$
98
99
100 $(1+(-2+3!)!)\cdot 4$
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