[seqfan] An amusing paradox?
rkg at cpsc.ucalgary.ca
Sun Apr 3 17:19:55 CEST 2011
A group of us have been investigating the Cookie
Monster Problem (P34 in The Inquisitive Problem
Solver, Vaderlind, Guy & Larson, MAA). The
Cookie Monster wants to empty all the cookie jars
with the least number of moves, where a move is
to select any subset of the jars and remove the
same (positive) number of cookies from each jar
in the subset.
I suggested `the first so many Fibonacci numbers'
as a possibly interesting set of numbers of cookies
in so many jars. Karen Seyffarth gave an efficient
algorithm: take the third largest number from
each of the three largest numbers of cookies. In
order to find a sequence which diverged a bit more
rapidly, I thought to take the sum of the previous
two terms PLUS ONE:
0+0+1=1, 0+1+1=2, 1+2+1=4, 2+4+1=7, 4+7+1=12, 7+12+1=21, ...
The Fibonacci numbers MINUS ONE! This is OEIS A000071.
Of course, it's only a matter of offset, which always
bewilders me. But not only me --- see remark by
J Perry, 2008-10-02. Best to all, R.
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