# Distinguish between 7, 13, 17, 19 with one question (answer 0, 1, 2, or 3) [closed]

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.

## closed as too broad by Wen1now, Rand al'Thor, Mike Earnest, Mithrandir, boboquackAug 22 '17 at 2:55

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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

• That is the exact solution I thought of! Two hours late of course... – Trenin Aug 21 '17 at 18:20

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.

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)