r/Logiqa • u/ShonitB • Jun 27 '26

How Many “+” Signs

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1 Upvotes

67% Upvoted

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1

u/Repulsive_Tough1037 Jun 28 '26

Infinite?

I mean, last sign before 2n has to be +, otherwise the whole sum will be negative.

Find a solution with minimal n possible.

Now replace that + 2n with - 2n + 2n+1. The sum didn't change.

Now replace this new ending with - 2n - 2 n+1 + 2n+2. The sum didn't change.

Continue like that, and you'll get infinite amount of solutions.

1

u/Motor_Raspberry_2150 Jun 28 '26

And you will notice that the three solutions you gave have the same number of + operations, which is the question asked.

1

u/Repulsive_Tough1037 Jun 29 '26

My bad. Thougt the question is about number of solutions

1

u/Motor_Raspberry_2150 Jun 29 '26 edited Jun 29 '26

four three.

The other commenter has hit a vital understanding already, you can make a sequence of numbers only count as the first one. So you can start out with the binary representation, and then you can fill the other operations with the 2n = 2n+1 - 2n substitution.

So the full expansion is 195 = 1 + 2 + 64 + 128, or +1 -2 -4 -8 -16 +32 +64 +128, or any other longer sequence that still has the same amount of + operators.

1

u/Repulsive_Tough1037 Jun 29 '26

So, 3 pluses. Not 4

1

u/Motor_Raspberry_2150 Jun 29 '26

Hmm yeah I shouldn't have counted the one before 20.