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Nine to One

9 8 7 6 5 4 3 2 1

You've probably seen the challenge called Make 100 or Make a Century. It gives you a string of the digits 1 through 9, and asks you to put plus (+) or minus (-) in between some of the digits to make an expression equal to 100.

1. This variation was suggested by Martin Gardner. Start with a string of digits running nine to one. Place either a plus or a minus between certain digits. A leading negative sign (-9) is not allowed. Other spaces may be left blank to create two- or three- digit numbers. For example,

98 – 76 + 5 – 4 + 3 – 21 = 5

but you must achieve the result one (1). The solution is not unique.

2. Can you use the same rules and achieve a zero result?

3. How many other totals can you make from 2 through 100 with these same rules?

Solution

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