3. #3 Prizewinners for a giveaway program are to be determined asfollows: Envelo

Question

3.      #3 Prizewinners for a giveaway program are to be determined asfollows:  Envelopesfor the first 500 entries will be numbered 1 through 500 and laidon a long table. The first official will walk along the table,opening all the envelopes. The second official will follow thefirst and close every even-numbered envelope.  Thethird official will follow the second, reversing every thirdenvelope by closing open envelopes and opening closedenvelopes.  Thefourth official will reverse every fourth envelope, and so on until500 officials have walked along the table and reversedenvelopes.  Theenvelopes that remain open after this procedure will be those ofthe contest winners.  Whatnumbers were on the winning envelopes?

Explanation / Answer

My algorithm is to use small population to do the trial. First I use 6 envelopes (c- close, o- open) o o o o o o o c o c o c o c c c o o o c c o o o o c c o c o o c c o c c Now I notice the every 3rd envelopes remains open Second I try 10 envelopes. o o o o o o o o o o o c o c o c o c o c o c c c o o o c c c o c c o o o o o c c o c c o c o o o c o o c c o c c o o c o o c c o c c c o c o o c c o c c c c c o o c c o c c c c o o o c c o c c c c o c So now it looks like not every 3rd envelopes. But now it lookslike 12, 22, 32 envelopesopen Let's try 17 envelopes o o o o o o o o o o o o o o o o o o c o c o c o c o c o c o c o c o o c c c o o o c c c o o o c c c o o c c o o o o o c c o c o c c o o o c c o c o o o c o o c o c o o o o c c o c c o o c o o o o c o o o o c c o c c c o c o o o o o o o o o c c o c c c c c o o o o o o c o o c c o c c c c o o o o o o o c o o c c o c c c c o c o o o o o c o o c c o c c c c o c c o o o o c o o c c o c c c c o c c c o o o c o o c c o c c c c o c c c c o o c o o c c o c c c c o c c c c c o c o o c c o c c c c o c c c c c c c o o c c o c c c c o c c c c c c o o o c c o c c c c o c c c c c c o c Yes!! now it proves 12, 22,32, and 42 envelopes are open so if there are 500 envelopes, the 12,22, 32 ...... 222 envelops areopen

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