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# How many different equations can be made with the numbers 0123?

A huge number.

0 + 1 + 2 = 3

0 + 2 + 1 = 3

1 + 0 + 2 = 3

1 + 2 + 0 = 3

2 + 0 + 1 = 3

2 + 1 + 0 = 3

-0 + 1 + 2 = 3 -0 + 2 + 1 = 3 1 - 0 + 2 = 31 + 2 - 0 = 32 - 0 + 1 = 32 + 1 - 0 = 3

0 - 1 + 3 = 2

0 + 3 - 1 = 2

-1 + 0 + 3 = 2

-1 + 3 + 0 = 2

3 + 0 - 1 = 2

3 - 1 + 0 = 2

-0 - 1 + 3 = 2-0 + 3 - 1 = 2-1 - 0 + 3 = 2-1 + 3 - 0 = 23 - 0 - 1 = 23 - 1 - 0 = 2

0 - 2 + 3 = 1

0 + 3 - 2 = 1

-2 + 0 + 3 = 1

-2 + 3 + 0 = 1

3 + 0 - 2 = 1

3 - 2 + 0 = 1

-0 - 2 + 3 = 1-0 + 3 - 2 = 1-2 - 0 + 3 = 1-2 + 3 - 0 = 13 - 0 - 2 = 13 - 2 - 0 = 1

1 + 2 - 3 = 0

1 - 3 + 2 = 0

2 + 1 - 3 = 0

2 - 3 + 1 = 0

-3 + 1 + 2 = 0

-3 + 2 + 1 = 0

For each of these equations there is a counterpart in which all signs have been switched. For example 0 + 1 + 2 = 3 gives -0 - 1 - 2 = -3and so on.

Now, all of the above equations has three numbers on the left and one on the right. Each can be converted to others with two numbers on each side. For example:the equation 0 + 1 + 2 = 3 gives rise to0 + 1 = 3 - 20 + 1 = -2 + 30 + 2 = 3 - 10 + 2 = -1 + 31 + 2 = 3 - 01 + 2 = -0 + 3-0 + 1 = 3 - 2-0 + 1 = -2 + 3-0 + 2 = 3 - 1-0 + 2 = -1 + 31 + 2 = 3 + 01 + 2 = +0 + 3

As you can see, the number of equations is huge!

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