# A Series That Totals 100? Impossible!

Use digits 0 to 9 (or 1 to 9), each once and only once, to make a total of 100. You might have played this game with your fellow-mates in school. Here are some examples that give 100 as the final answer:

100 = 123 – 45 – 67 + 89

100 = 123 – 4 – 5 – 6 – 7 + 8 – 9

100 = 123 + 4 – 5 + 67 – 89

100 = 123 + 45 – 67 + 8 – 9

100 = 98 – 76 + 54 + 3 + 21

100 = 140 – 2 – 3 – 5 – 6 – 7 – 9 – 8

100 = 194 – 78 – 2 – 3 – 5 – 6 – 0

100 = 284 – 96 – 57 – 31 – 0

100 = 1 + 2 + 3 – 4 + 5 + 6 + 78 + 9

100 = 1 + 2 + 34 – 5 + 67 – 8 + 9

100 = 12 + 3 – 4 + 5 + 67 + 8 + 9

You may notice that none of the above expressions use only addition to get 100. Why so? Can we write a series of numbers whose sum is 100?

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