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First, write an expression using exactly one 3 and exactly one 4 to make 24.

Second, write an expression using exactly one 3 and exactly one 4 to make 30.

Math You Can Use for each problem:

  • Division
  • Factorials (just for regular factorial use, no special factorials)
  • Parentheses (They would be required to show the factorial of a factorial, as in (X!)!, for instance.)

Other Rules For Clarification:

  • No other digits may be used.
  • No other operations may be used.

I am intending one solution for each problem.

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  • 4
    $\begingroup$ I think this puzzle would have been more interesting with a larger space of possibilities. With two numbers, a unary operator, and a binary operator, the only possible solutions take the factorial of 3 some number of times (possibly zero), likewise for 4, and divide the results. It's straightforward to write out all the small possibilities. $\endgroup$ – xnor Jun 26 '15 at 18:51
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30:

$(3!)!\div4! = 30$

24:

$(4!\div3!)! = 24$

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0
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Shamelessly stolen from Tim!!

24:

$\frac{4!}{3!}!$

Cheating way:

$3!4$

30:

$\frac{3!!}{4!}$

More clearly:

$\frac{(3!)!}{4!}$

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