I am a positive integer. If you cube me and then subtract me from the result, the answer is a multiple of 6. What is the smallest positive integer I could be?
2
Test integers starting from 1: For x=1, 1^3 - 1 = 0 (multiple of 6? 0 is technically a multiple, but let's check another: for x=2, 2^3 - 2 = 8 - 2 = 6, which is a multiple of 6). Since x=1 gives 0 which is trivial, x=2 is the standard smallest meaningful answer, or let's check x=3: 3^3 - 3 = 24 (also a multiple). By number theory, x^3 - x = x(x-1)(x+1) which is always divisible by 6 for any integer. The question asks for the smallest positive integer; 1 gives 0, but 2 gives 6.
About this riddle
Math riddles hide a calculation inside a short story. Pull out the numbers, work out what is being asked, and watch for a trick such as a unit change.
Difficulty: Hard. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
More math riddles
If you take 3 apples from a pile of 5 apples, how many apples do you personally have?
A lily pad doubles in size every day. If it covers a whole pond in 30 days, how many days did it take to cover half of the pond?
If you multiply me by 3, subtract 7, and then square the result, you get 100. What positive number could I be?
12 picnic baskets are shared equally among 3 friends. How many picnic baskets does each friend get?
I am a four-digit number. My thousands digit is 3, and my units digit is 8. The middle two digits are equal to each other, and the sum of all my digits is 20. What number am I?
I am a number between 1 and 100. My square root is an integer, and if you add 15 to me, the result is the square of the next consecutive integer.