Below is an equation that is not correct yet. By adding a number of plus signs and minus signs between the digits on the left side (without changes the order of the digits), the equation can be made correct. 123456789 = 100
The Question: How many different ways are there to make the equation correct?
One way: 123 - 45 - 67 + 89 = 100. Can you give a systematic way to find answers ?
123 + 45 -67 +89 = 100 1 + 2 - 3 + 4 + 5 + 6 + 78+ 9 = 100
12 + 3 - 4 + 5 + 67 + 89 = 100 1 + 2 + 34 - 5 + 67 - 8 + 9 =100
1 + 23 - 4 +5 +6 +78 -9 = 100 1 + 2 + 3 - 4 + 5 + 6 + 78 + 9 = 100
12 -3 - 4 + 5 - 6 + 7 + 89 = 100 12 + 3 4 + 5 -6 - 7 + 89 = 100
1 + 23 - 4 + 56 + 7 + 8 + 9 = 100
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