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Negative 20/20

Use the digits 1, 2, 3 and 4 exactly once each, and the symbols +, –, *, /, ( ), ^ (exponentiation) and the decimal point to create expressions for the integers in the interval from -20 through +20. A leading negative sign is not permitted. Your expressions must follow the standard order of operations.

Good examples in other intervals would be:
1 – 4(3*2) = -23

34 + 2 + 1 = 37

Examples not permitted are:

(4 ^ 2) – 2 + 3 – 1 = 16 (uses 2 twice)
4 * 2 / 3 + 1 = 2 (incorrect order of operations)
-4(2) – 3 = -11 (uses a leading negative sign and repeats a digit)

As you can see, some of the useful symbols are parentheses and subtraction signs. Write a reflection on the strategies you found useful and the experience in general. Hints (optional) below.

Hints: Don’t try to work in order. You will get most of them by the “try something” and the “change one thing” strategies.

Solution

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