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# How do we respond?

## Question

I remember seeing a couple posts similar to this one some time back and thought I'd try my hand at one.

Here is the situation:

While scanning space for signs of life a group of scientists receive a series of messages the last of which requires a response. The messages are translated as follows:

12 % 10 = 8

4 % 6 = 4

9 % 7 = 6

11 % 13 = 6

5 % 15 = 2

14 % 16 = ___

What number do we need to respond with?

you have to figure out what operation(s) are done with the two numbers to get the last number.

## Recommended Posts

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I started with ANDing the binary representations, but it worked only for the first two. Good puzzle.

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I tried this:

(12-8)-(10-8)=2

(4-4)-(6-4) =-2

(9-6)-(7-6) =2

(11-6)-(13-6)=-2

but this role does not work with 5%15=2

otherwise, the missing number should be =0

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I tried this:

(12-8)-(10-8)=2

(4-4)-(6-4) =-2

(9-6)-(7-6) =2

(11-6)-(13-6)=-2

but this role does not work with 5%15=2

otherwise, the missing number should be =0

but an interresting relationship between the numbers. Unfortunately 0 isn't correct, but you can get the correct answer using your method.

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