# 24 Puzzle Solution

when play 24 puzzle, please show me how to calculate to 24 using 6 3 1 4

The 24 puzzle is a fun and challenging game where you need to use the four given numbers with any combination of addition, subtraction, multiplication, and division to make the total 24. Let's use the numbers 6, 3, 1, and 4 to reach 24.

A good strategy is to look for combinations of numbers that can easily be manipulated to reach 24. Remember, you can use each number only once.

Let's try this combination:

- Multiply 6 and 4 to get 24 (6 * 4 = 24).
- Now, the other two numbers are 3 and 1. If we add them, we get 4 (3 + 1 = 4).
- However, since we've already reached 24 in the first step and don't want to change that, let's find a way to use 3 and 1 without affecting our 24.

We can do this by multiplying the result of 3 + 1 (which is 4) by 1. Multiplying anything by 1 doesn't change its value. So, we can safely say:

[ 6 \times 4 \times (3 + 1) \div 4 = 24. ]

This way, we have used all the numbers: 6, 3, 1, and 4, and the operations of multiplication, addition, and division to make 24.

If you have any more numbers or puzzles, feel free to ask!

you need all 4 numbers to calculate once and only once

Understood, let's use each of the numbers 6, 3, 1, and 4 exactly once to make 24. Let's try a different approach:

- Start by adding 3 and 1, which gives us 4 (3 + 1 = 4).
- Now, multiply this result by 4 (from our given numbers). This gives us 16 (4 × 4 = 16).
- Finally, add this result to 6 to get 24 (16 + 6 = 24).

So, the calculation would be: ((3 + 1) \times 4 + 6 = 24.)

This way, each of the numbers 6, 3, 1, and 4 is used exactly once. Would you like to try another set of numbers or have any other questions about math puzzles?