## Problem #020 - make 24 with 3 3 8 8

Today we are visiting a specific instance of a well-known basic mathematics game, the 24 Game. The "24 Game" is usually played with younger students because it helps them develop skills related to the basic arithmetic operations.

# Problem statement

The "24 Game" is usually played with four different numbers from $$1$$ to $$9$$, for example drawn randomly out of a small deck with those numbers. For this blog post, you can forget about all that, I picked very specific numbers for you.

Using the four numbers $$3$$, $$3$$, $$8$$ and $$8$$ and the four arithmetic operations addition, subtraction, multiplication and division, you have to make an expression that evaluates to $$24$$. The rules are simple:

• each number must be used exactly once;
• operations can be used any number of times (even zero times);
• the precedence of operations can be changed by the use of $$()$$;
• numbers cannot be used by positioning them in a special way, e.g. you can't make $$33$$ by joining the two $$3$$s and you can't make $$27$$ by writing $$3^3$$.

I am not giving you a puzzle with a cheap trick involved. This is pure arithmetics.

An example valid expression would be $$(3+3)\times (8+8)$$ except this is not the solution because it gives $$96$$ instead of $$24$$.

I heard of this from the same friend who told me about the "Fold the alphabet" problem.

## Hint

Do not read the hint if you haven't spent some time thinking about the problem yet!

# Solution

There really is no point in sugar coating this for you, the solution is the expression $$8 \div (3 - 8\div 3)$$. Quite ingenious, isn't it?