# Make 24 and 30 using the digits 3 and 4

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.

• 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. – xnor Jun 26 '15 at 18:51

30:

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

24:

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

# Shamelessly stolen from Tim!!

24:

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

Cheating way:

$3!4$

30:

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

More clearly:

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