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I am thinking of a prime number, either 7 or 13 or 17 or 19.

You can ask me only one question to which the answer I give must be either 0 or 1 or 2 or 3. Can you then tell what number I am thinking?

Conditions: Please don't ask a question on the progression order of the numbers like "If you consider 23 as the 4th number in a progression of Prime numbers, and discard 11, what progression number will you get". In this case 19 would be 3rd, 17 would be 2nd etc. Also you cannot assign values to the 4 numbers. For example "If 7 is 0, 13 is 1, 17 is 2 etc" - that will be too simple.

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Take your number modulo 8, subtract 1 and divide by 2. 0 -> 17, 1-> 19, 2-> 13, 3-> 7.

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  • 1
    $\begingroup$ That is the exact solution I thought of! Two hours late of course... $\endgroup$ – Trenin Aug 21 '17 at 18:20
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Here is my question:

How many zeros (excluding leading) are in the base 2 representation of your number? 7->111, zero 0's. 13->1101, one 0. 17->10001, three 0's. 19->10011, two 0's.

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using 2 steps, what is your final answer.

Step 1:

The prime you are thinking off subtract 4:7-4=3,13-4=9,17-4=13,19-4=15.

Step 2:

Divide by 5 and do not worry about remainders i.e. take the integer value of your answer.3/5=0 (Prime = 7),9/5=1(Prime = 13),13/5=2 (Prime = 17),15/5=3 (Prime = 19)

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