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From 1 to 9

From 1 to 9

Given the numbers 1 2 3 4 5 6 7 8 9 insert the + or - signs between them so that the result is 1 using all the numbers only once.

How many different solutions are you able to find?

Solution

In total there are 23 different solutions:

  • -1 - 2 - 3 - 4 - 5 + 6 - 7 + 8 + 9 = 1
  • -1 - 2 - 3 + 4 + 5 + 6 - 7 + 8 - 9 = 1
  • -1 - 2 + 3 - 4 + 5 - 6 + 7 + 8 - 9 = 1
  • -1 - 2 + 3 - 4 + 5 + 6 - 7 - 8 + 9 = 1
  • -1 - 2 + 3 + 4 - 5 - 6 + 7 - 8 + 9 = 1
  • -1 + 2 - 3 - 4 - 5 + 6 + 7 + 8 - 9 = 1
  • -1 + 2 - 3 - 4 + 5 - 6 + 7 - 8 + 9 = 1
  • -1 + 2 - 3 + 4 - 5 - 6 - 7 + 8 + 9 = 1
  • -1 + 2 + 3 - 4 + 5 + 6 + 7 - 8 - 9 = 1
  • -1 + 2 + 3 + 4 - 5 + 6 - 7 + 8 - 9 = 1
  • -1 + 2 + 3 + 4 + 5 - 6 - 7 - 8 + 9 = 1
  • 1 - 2 - 3 - 4 - 5 + 6 + 7 - 8 + 9 = 1
  • 1 - 2 - 3 - 4 + 5 - 6 - 7 + 8 + 9 = 1
  • 1 - 2 - 3 + 4 + 5 + 6 + 7 - 8 - 9 = 1
  • 1 - 2 + 3 - 4 + 5 + 6 - 7 + 8 - 9 = 1
  • 1 - 2 + 3 + 4 - 5 - 6 + 7 + 8 - 9 = 1
  • 1 - 2 + 3 + 4 - 5 + 6 - 7 - 8 + 9 = 1
  • 1 + 2 - 3 - 4 + 5 - 6 + 7 + 8 - 9 = 1
  • 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 = 1
  • 1 + 2 - 3 + 4 - 5 - 6 + 7 - 8 + 9 = 1
  • 1 + 2 + 3 - 4 - 5 - 6 - 7 + 8 + 9 = 1
  • 1 + 2 + 3 + 4 - 5 + 6 + 7 - 8 - 9 = 1
  • 1 + 2 + 3 + 4 + 5 - 6 - 7 + 8 - 9 = 1