Each step I take doubles the footprints left by the previous step. I start with 1 footprint on step one, 2 footprints on step two, and so on. On which step will I have created a total cumulative count of exactly 1,023 footprints?
Step 10
The sum of powers of 2 from 2^0 to 2^(n-1) equals 2^n - 1. For a cumulative total of 1,023 footprints, 2^n - 1 = 1023, which means 2^n = 1024, so n = 10.
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: Medium. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
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