Beautiful Number Pattern
Start with the sequence of non-zero digits 123456789. The problem is to place plus or minus signs between them so that the result of thus described arithmetic operation will be 100.
1 + 2 + 34 - 5 + 67 - 8 + 9 = 100
12 + 3 - 4 + 5 + 67 + 8 + 9 = 100
123 - 4 - 5 - 6 - 7 + 8 - 9 = 100
123 + 4 - 5 + 67 - 89 = 100
123 + 45 - 67 + 8 - 9 = 100
123 - 45 - 67 + 89 = 100
12 - 3 - 4 + 5 - 6 + 7 + 89 = 100
12 + 3 + 4 + 5 - 6 - 7 + 89 = 100
1 + 23 - 4 + 5 + 6 + 78 - 9 = 100
1 + 23 - 4 + 56 + 7 + 8 + 9 = 100
1 + 2 + 3 - 4 + 5 + 6 + 78 + 9 = 100
If we put a "-" before 1, we have one more solution:
-1 + 2-3 + 4 + 5 + 6 + 78 + 9 = 100
Using the "." decimal separation I found another solution:
1 + 2.3 - 4 + 5 + 6.7 + 89 = 100
What about 987654321 ?
98 - 76 + 54 + 3 + 21 = 100
9 - 8 + 76 + 54 - 32 + 1 = 100
98 + 7 + 6 - 5 - 4 - 3 + 2 - 1 = 100
98 - 7 - 6 - 5 - 4 + 3 + 21 = 100
9 - 8 + 76 - 5 + 4 + 3 + 21 = 100
98 - 7 + 6 + 5 + 4 - 3 - 2 - 1 = 100
98 + 7 - 6 + 5 - 4 + 3 - 2 - 1 = 100
98 + 7 - 6 + 5 - 4 - 3 + 2 + 1 = 100
98 - 7 + 6 + 5 - 4 + 3 - 2 + 1 = 100
98 - 7 + 6 - 5 + 4 + 3 + 2 - 1 = 100
98 + 7 - 6 - 5 + 4 + 3 - 2 + 1 = 100
98 - 7 - 6 + 5 + 4 + 3 + 2 + 1 = 100
9 + 8 + 76 + 5 + 4 - 3 + 2 - 1 = 100
9 + 8 + 76 + 5 - 4 + 3 + 2 + 1 = 100
9 - 8 + 7 + 65 - 4 + 32 - 1 = 100
1 + 2 + 34 - 5 + 67 - 8 + 9 = 100
12 + 3 - 4 + 5 + 67 + 8 + 9 = 100
123 - 4 - 5 - 6 - 7 + 8 - 9 = 100
123 + 4 - 5 + 67 - 89 = 100
123 + 45 - 67 + 8 - 9 = 100
123 - 45 - 67 + 89 = 100
12 - 3 - 4 + 5 - 6 + 7 + 89 = 100
12 + 3 + 4 + 5 - 6 - 7 + 89 = 100
1 + 23 - 4 + 5 + 6 + 78 - 9 = 100
1 + 23 - 4 + 56 + 7 + 8 + 9 = 100
1 + 2 + 3 - 4 + 5 + 6 + 78 + 9 = 100
If we put a "-" before 1, we have one more solution:
-1 + 2-3 + 4 + 5 + 6 + 78 + 9 = 100
Using the "." decimal separation I found another solution:
1 + 2.3 - 4 + 5 + 6.7 + 89 = 100
What about 987654321 ?
98 - 76 + 54 + 3 + 21 = 100
9 - 8 + 76 + 54 - 32 + 1 = 100
98 + 7 + 6 - 5 - 4 - 3 + 2 - 1 = 100
98 - 7 - 6 - 5 - 4 + 3 + 21 = 100
9 - 8 + 76 - 5 + 4 + 3 + 21 = 100
98 - 7 + 6 + 5 + 4 - 3 - 2 - 1 = 100
98 + 7 - 6 + 5 - 4 + 3 - 2 - 1 = 100
98 + 7 - 6 + 5 - 4 - 3 + 2 + 1 = 100
98 - 7 + 6 + 5 - 4 + 3 - 2 + 1 = 100
98 - 7 + 6 - 5 + 4 + 3 + 2 - 1 = 100
98 + 7 - 6 - 5 + 4 + 3 - 2 + 1 = 100
98 - 7 - 6 + 5 + 4 + 3 + 2 + 1 = 100
9 + 8 + 76 + 5 + 4 - 3 + 2 - 1 = 100
9 + 8 + 76 + 5 - 4 + 3 + 2 + 1 = 100
9 - 8 + 7 + 65 - 4 + 32 - 1 = 100
Credits to Electrified Theophilus on Math Quiz
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