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Saturday, July 26, 2008

Plus & Minus

Below is an equation that isn't correct yet. By adding a number of plus signs and minus signs between the ciphers on the left side (without changes the order of the ciphers), the equation can be made correct.

123456789 = 100

The Question: How many different ways are there to make the equation correct?


Answer: There are 11 different ways:

123+45-67+8-9=100
123+4-5+67-89=100
123-45-67+89=100
123-4-5-6-7+8-9=100
12+3+4+5-6-7+89=100
12+3-4+5+67+8+9=100
12-3-4+5-6+7+89=100
1+23-4+56+7+8+9=100
1+23-4+5+6+78-9=100
1+2+34-5+67-8+9=100
1+2+3-4+5+6+78+9=100

Remark: if it is not only allowed to put plus signs and minus signs between the ciphers, but also in front of the first 1, then there is a twelfth possibility: -1+2-3+4+5+6+78+9=100.


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