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Question Number 170240 by otchereabdullai@gmail.com last updated on 18/May/22

A deck of 2022 cards is numbered 1 to 2022. The first, 1, is placed at the bottom of the deck , the second,2, is discarded, the third ,3, placed at the bottom, the next,4, is discarded, and so on. the process continue till only one card is left. What is the number on the card? can you generalise? try some simpler example to help.

$$\:\mathrm{A}\:\mathrm{deck}\:\mathrm{of}\:\mathrm{2022}\:\mathrm{cards}\:\mathrm{is}\:\mathrm{numbered} \\ $$$$\:\mathrm{1}\:\mathrm{to}\:\mathrm{2022}.\:\mathrm{The}\:\mathrm{first},\:\mathrm{1},\:\mathrm{is}\:\mathrm{placed}\:\mathrm{at}\: \\ $$$$\:\:\:\mathrm{the}\:\mathrm{bottom}\:\mathrm{of}\:\mathrm{the}\:\mathrm{deck}\:,\:\mathrm{the}\: \\ $$$$\mathrm{second},\mathrm{2},\:\mathrm{is}\:\mathrm{discarded},\:\mathrm{the}\:\mathrm{third}\:,\mathrm{3},\: \\ $$$$\mathrm{placed}\:\mathrm{at}\:\mathrm{the}\:\mathrm{bottom},\:\mathrm{the}\:\mathrm{next},\mathrm{4},\:\mathrm{is}\: \\ $$$$\:\mathrm{discarded},\:\mathrm{and}\:\mathrm{so}\:\mathrm{on}.\:\mathrm{the}\:\mathrm{process}\: \\ $$$$\mathrm{continue}\:\mathrm{till}\:\mathrm{only}\:\mathrm{one}\:\mathrm{card}\:\mathrm{is}\:\mathrm{left}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:\mathrm{on}\:\mathrm{the}\:\mathrm{card}?\: \\ $$$$\mathrm{can}\:\mathrm{you}\:\mathrm{generalise}?\:\mathrm{try}\:\mathrm{some}\:\mathrm{simpler} \\ $$$$\mathrm{example}\:\mathrm{to}\:\mathrm{help}. \\ $$$$\: \\ $$

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