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Would you like to play a game? (Posted on 2004-05-10) Difficulty: 4 of 5
Bologna Sandwich was worried about an upcoming test in Discrete Mathematics and was finding it hard to get to sleep. Bologna awoke early in the morning, aroused by devilish laughter, only to see an impish looking homunculus sitting at the bottom of the bed next to a seemingly infinite pile of chips. Hello, Bologna, it said, would you like to play a little game? This pile contains 43546758443209876 chips and the bottom chip represents your immortal soul. The rules are quite simple. The first player removes some chips, but not all of them. After that we take turns removing some chips.

The only rule now is that a player cannot remove more than the previous player removed in his last turn. The winner is the player who takes the last chip. If I win I get to keep your soul and if you win, you get an A in the test. Would you like to go first or second? This seemed a reasonable bet to Bologna.

Can you give Bologna a strategy for playing no matter how many chips there are? (What if there were just one more chip in the initial pile?)

What if the rule were that one is allowed to take up to twice the number of chips the previous player took?

No Solution Yet Submitted by SilverKnight    
Rating: 4.3333 (3 votes)

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re(2): Doubling case Solved | Comment 11 of 13 |
(In reply to re: Doubling case Solved by Jer)

Fibonacci numbers:

 2 
 3
 5
 8
 13
 21
 34
 55
 89
 144
 233
 377
 610
 987
 1597
 2584
 4181
 6765
 10946
 17711
 28657
 46368
 75025
 121393
 196418
 317811
 514229
 832040
 1346269
 2178309
 3524578
 5702887
 9227465
 14930352
 24157817
 39088169
 63245986
 102334155
 165580141
 267914296
 433494437
 701408733
 1134903170
 1836311903
 2971215073
 4807526976
 7778742049
 12586269025
 20365011074
 32951280099
 53316291173
 86267571272
 139583862445
 225851433717
 365435296162
 591286729879
 956722026041
 1548008755920
 2504730781961
 4052739537881
 6557470319842
 10610209857723
 17167680177565
 27777890035288
 44945570212853
 72723460248141
 117669030460994
 190392490709135
 308061521170129
 498454011879264
 806515533049393
 1304969544928657
 2111485077978050
 3416454622906707
 5527939700884757
 8944394323791464
 14472334024676221
 23416728348467685
 37889062373143906
 61305790721611591
 99194853094755497
 160500643816367088
 259695496911122585
 420196140727489673
 679891637638612258
 1100087778366101931
 1779979416004714189
 2880067194370816120
 4660046610375530309
 7540113804746346429
 12200160415121876738
 19740274219868223167
 31940434634990099905
 51680708854858323072
 83621143489848422977
 135301852344706746049
 218922995834555169026
 354224848179261915075
 573147844013817084101
 927372692193078999176

So 43546758443209876 is not Fibonacci.  The next lower number that is Fibonacci is 37889062373143906.


  Posted by Charlie on 2004-05-11 09:18:34
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