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Logic Level 4

9   8   7   6   5   4   3   2   1   =  100\LARGE 9 \ \ \ 8 \ \ \ 7 \ \ \ 6 \ \ \ 5 \ \ \ 4 \ \ \ 3 \ \ \ 2 \ \ \ 1 \ \ \ = \ \ 100

Without touching the right side of the equation, find a way to make the equation above true. You are only allowed to use mathematical operators like addition and subtraction only.

Find a possible way to make the above equation true such that you used the least number of mathematical operators. Let AA denote the number of addition signs used and SS denote the number of subtraction sign used. Find the value of 3A+4S3A+4S.

Details And Assumptions:

  • As an explicit example if the equation 9+8765+4+321=1009+8-7-6-5+4+3-2-1=100 is true, then you have used 4 addition signs and 5 subtraction signs. So A=4 , S=5A=4 \ , \ S=5.

  • You can combine the digits as well.That is 98765+43+2198765+43+21.

  • You must keep the digits in order (from left to right).That is 9+87+65+43219+87+65+4321 is valid but 9+78+56+34219+78+56+3421 is not allowed.

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