# Use all of the following symbols and numbers in one equation

Use all of the following symbols and numbers in one equation for the result to be equal to 10

(14, 12, 9 , 7, 3) (÷ × - ÷)

• Any limits on using parentheses? Apr 25 '20 at 21:46

This works:

$$12 ÷ 3 = 4$$
$$9 - 4 = 5$$
$$14 ÷ 7 = 2$$
$$5 * 2 = 10$$

And in one equation (assuming the two parentheses around the symbols are included):

$$(9 - 12 ÷ 3) * 14 ÷ 7 = 10$$

• Even more precisely, that should be written without parentheses enclosing 12/3 or 14/7 since only two pairs of parentheses are given. Apr 25 '20 at 21:36
• @trolley813 I'm not sure if the parenthenses are part of the symbols included, or if they are just showing the set of symbols because there's parentheses around the numbers too. Thanks for the suggestion! The equation does now work with just two parentheses, assuming those are included Apr 25 '20 at 21:40

# With no parentheses

I checked all arrangments; no solution.

# With one parenthesis pair

I didn't check exhaustively for all solutions, but these work. $$(9-3/7)/12*14 = 10$$ $$(9-3/7)*14/12 = 10$$ $$(9-12/3)/7*14 = 10$$ $$(9-12/3)*14/7 = 10$$

# With two parenthesis pairs

If the answer really must have two pairs of parentheses because they are among the symbols shown along with the numbers and operators, then we can trivially convert the one-pair solutions to match that. $$(9-3/7)/12*(14) = 10$$ $$(9-3/7)*(14/12) = 10$$ $$(9-12/3)/7*(14) = 10$$ $$(9-12/3)*(14/7) = 10$$