Q: Name five two-digit numbers that are evenly spaced out — like 32, 34, 36, 38 and 40 — in which all 10 digits from 0 to 9 are used once each. What numbers are these?The first answer came to me as I was driving and listening to the puzzle. However, as I was typing this clue, I came up with another answer that also works. How to give a clue without giving it away, I don't know.
Edit: The clues were to driving which should have made you think of either a car (ie. Car 54) or golf (ie. 18 holes). Those were the starting numbers of two of the four possible sequences.
The tens digit will either step by 1 (5,6,7,8,9) or by 2 (1,3,5,7,9) always ending on 9. The ones digit will also step by 1 (0,1,2,3,4) or by 2 (0,2,4,6,8) always starting (or ending) on 0. That leads to 4 possible sequences:
Starting with 10 stepping by 22 (20+2)
Starting with 18 stepping by 18 (20-2)
Starting with 50 stepping by 11 (10+1)
Starting with 54 stepping by 9 (10-1)
A: There are four possible sequences of two-digit numbers: