Below is an equation that isn’t correct yet, With the addition of several plus signs and minus signs between the digits on the left side (without changes an order of the digits), the equation can be done correct.
1 2 3 4 5 6 7 8 9 = 100
Question: How many different ways are there to make the equation correct?
Solution : ↓
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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 digits, 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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