49. Summing Expenses and Remainders Puzzle You start with 50 rupees. You spend 20 rupees, leaving you with 30 rupees. Then you spend 15 rupees, leaving you with 15 rupees. Next, you spend 9 rupees, leaving you with 6 rupees. Finally, you spend 6 rupees. The total of your expenses is 50 rupees, but if you (mistakenly) add up the amounts you had left after each spending step (30 + 15 + 6 + 0), you get 51 rupees. How can this be? Added 11 August 2016 Show Solution Solution: The ‘51 rupees’ comes from an invalid addition of overlapping leftovers. After each spend you have less money than before, but those leftover amounts are not disjoint portions of your original 50 rupees—they are successive remainders of the same pool. You cannot add them together. The correct total spent is 20 + 15 + 9 + 6 = 50 rupees, and the final remainder is 0. The 51 rupees arises only if you mistakenly sum the successive remainders (30 + 15 + 6 + 0), which is a logical error, not a real extra rupee.
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