What Can Plus/Minus Get Us?

Logic Level 3

1 □ 2 □ 3 □ 4 □ 5 □ 6 □ 7 \Large 1 \ \square \ 2 \ \square \ 3 \ \square \ 4 \ \square \ 5 \ \square \ 6 \ \square \ 7

If we only used + \large \color{#3D99F6}{+} and − \large \color{#D61F06}{-} in place of the boxes above, how many distinct values can we obtain?

Inspiration .

64 62 26 28

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Calvin Lin by Calvin Lin

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1 solution

Jaskeerat Singh
Oct 26, 2015

The total can vary from -26 to +28. Now total can be even only (any change of sign changes it by twice of number. Also 26 is not possible. So total formations 26.

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And what about the total equal to zero?

Ricardo Takayama - 5 years, 7 months ago

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It's already being counting.

28 , 24 , 22 , 20 , 18 , 16 , 14 , 12 , 10 , 8 , 6 , 4 , 2 , 0 , − 2 , − 4 , − 6 , − 8 , − 10 , − 12 , − 14 , − 16 , − 18 , − 20 , − 22 , − 26. 28, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, -12, -14, -16, -18, -20, -22, -26.

The funny thing about this question it that when you have a subtraction, it decreases the double of the value of the negative number. The same happens with the opposite, when you have a sum, it increases the double of the positive number. With 3 3 even numbers, 3 3 odd numbers, the result will be an even number.

Marco Antonio - 5 years, 5 months ago

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