For example,
1 + 2 + 3 + – 4 + 5 + 6 + 78 + 9 = 100
Can you obtain a total of 100 using fewer plus or minus signs than in the given example?
You could get rid of the + in front of -4. It would not change a thing.
1--- 1 + 2 + 3 + 4 + 5 + 6 + 7 + (8X9) = 100
2--- -(1X2) - 3 - 4 - 5 + (6x7) + (8X9) = 100
3--- 1 + (2X3) + (4x5) - 6 + 7 + (8x9) = 100
4--- (1 + 2 - 3 - 4)x(5 - 6 - 7 - 8 - 9) = 100
5--- (1 +(2x3) + 4 + 5 + 67 + 8 + 9 = 100
6--- (1X2) + 34 + 56 + 7 - 8 + 9 = 100
7--- 12+ 3 - 4 + 5 + 67 + 8 + 9 = 100
8--- 123- 4 - 5 - 6 - 7 + 8 - 9 = 100
9--- 123 + 4 - 3 + 67 - 8 - 9 = 100
10--- 123 + 45 - 67 + 8 - 9 = 100
11--- 123 - 45 - 67 + 89 = 100 WOW
You might also be surprised to see that it can be done in the reverse also.
1-- 98 - 76 + 54 + 3 + 21 = 100
2-- 9 - 8 + 76 + 54 - 32 + 1 = 100
3-- 9 - 8 + 7 + 65 - 4 + 32 - 1 = 100
4-- 9 - 8 + 76 - 5 + 4 + 3 + 21 = 100
5-- 98 - 7 - 6 - 5 - 4 + 3 + 21 = 100
6-- 9 + 8 + 76 + 5 + 4 - 3 + 2 - 1 = 100
7-- 9 + 8 + 76 + 5 - 4 + 3 + 2 + 1 = 100
8-- 98 + 7 + 6 - 5 - 4 - 3 + 2 - 1 = 100
9-- 98 + 7 - 6 + 5 - 4 - 3 + 2 + 1 = 100
10-- 98 + 7 - 6 + 5 - 4 + 3 - 2 - 1 = 100 To name a few.
No it's the other way around Get it?
To solve this problem, we need to find an expression with fewer plus or minus signs that equals 100. Let's try to simplify the original expression and see if we can come up with a shorter alternative.
1 + 2 + 3 + -4 + 5 + 6 + 78 + 9 = 100
Let's remove some numbers and see if the sum remains 100:
1 + 2 + -4 + 5 + 6 + 9 = 19
As you can see, this sum is significantly smaller than 100. So, we need to rearrange the numbers in a different way to reach our target.
Let's try to modify the original expression in another manner:
1 + 2 - 3 + 4 + 5 + 67 + 8 - 9 = 75
Unfortunately, this sum is also lower than 100. We must continue searching for alternative arrangements.
After several attempts, it becomes evident that it is not possible to obtain a sum of 100 with fewer plus or minus signs than the given example. The initial expression is the most concise way to reach a sum of 100 using the numbers 1 through 9.