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Try to make all numbers 1-30 using the digits 2, 0, 2, 5.

Rules:

Use all four digits exactly once.

Allowed operations: $+,−,×,÷,! \text{ (factorial)}, !! \text{ (double factorial)}, !!! \text{ (triple factorial)} , x^y \text{ (exponentiation)}, \sqrt{x} \text{ (square root).}$

Parentheses and concatenation are allowed. (e.g. 20+(2∗5)).

Squaring uses the digit 2.

Keep the order "2, 0, 2, 5" in all expressions.

The modulus operator is not allowed.

Rounding is not allowed.

Follow up: Can you continue till 100?

Inspired by this question

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3
  • 1
    $\begingroup$ I don't find these "Make numbers 1..30" questions interesting. Most of the expressions are too easy and there are to many answers. A better way would be to search for one specially difficult number to form and ask to find how it can be made. $\endgroup$
    – Florian F
    Feb 5 at 10:30
  • 1
    $\begingroup$ Also, you're a year early. $\endgroup$
    – Bass
    Feb 5 at 20:59
  • $\begingroup$ @Bass I was wondering about how you would get the answer with 2 0 2 5. Is that bad? $\endgroup$
    – WOWOW
    Feb 5 at 22:27

1 Answer 1

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I haven't used $\sqrt{\ }$, nor any double/triple factorial.

$1 = -2+0-2+5\\2 = 2+0*2*5\\3 = -2+0*2+5\\4 = 2-0!-2+5\\5 = 2+0-2+5\\6 = 2+0!-2+5\\7 = 2*0+2+5\\8 = -2+0+2*5\\9 = 2+0+2+5\\10= 2*0+2*5\\11= 2^0+2*5\\12= 2+0+2*5\\13= 20-2-5\\14= 2*(0+2+5)\\15= (2-0!+2)*5\\16= 2*(0!+2+5)\\17= 20+2-5\\18= 2*(-0!+2*5)\\19= (2+0+2)!-5\\20= (2+0+2)*5\\21= (2+0!)*(2+5)\\22= 2*(0!+2*5)\\23= 20-2+5\\24= (2-0!-2+5)!\\25= (2+0!+2)*5\\26= 2^0+25\\27= 20+2+5\\28= 2+0!+25\\29= (2+0+2)!+5\\30= 2*(0!+2)*5$
Thanks to Bass for getting rid of the use of double factorial in 26 and 28.

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  • $\begingroup$ Nice. Try the follow up. I think you can do it. $\endgroup$
    – WOWOW
    Feb 5 at 8:40
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    $\begingroup$ How about "2^0+25" and "2+0!+25" instead of the clunky double factorials? $\endgroup$
    – Bass
    Feb 5 at 21:06
  • $\begingroup$ @Bass Oh, of course. I keep forgetting concatenation. $\endgroup$ Feb 5 at 22:37

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