So, It seems that the pattern is: C = A XOR B i.e. the number in position C is the result of the XOR between the previous two numbers (of course the first two numbers of the sequence - 5 and 10 - are given).

So, an algo could be to generate the sequence of all the possible binary numbers using the previous pattern until we reach the input number (so it is a multiplo of 5). As soon as we generate a bigger number we stops saying that the number is not a multiple of 5.

Here the first five multiple of 5:

ReplyDelete00101

01010

01111

10100

11001

...

So, It seems that the pattern is: C = A XOR B i.e. the number in position C is the result of the XOR between the previous two numbers (of course the first two numbers of the sequence - 5 and 10 - are given).

So, an algo could be to generate the sequence of all the possible binary numbers using the previous pattern until we reach the input number (so it is a multiplo of 5). As soon as we generate a bigger number we stops saying that the number is not a multiple of 5.

The above logic fails. 20 is not from 10 XOR 15.

ReplyDeleteIt is matter of checking last digit. Get the remainder mod 5. If it is 0 or 5, number is multiple of 5.