Each issue Jerry, O4R's puzzle guy, brings you a set of puzzles. As always, the answers will be published in the next issue. They are now posted here as well! Questions and discussion may be directed to Jerry.
OK, here's an easy(er) one for openers.
Let's say you have 1,000 one dollar bills and 10
envelopes. Figure out how to distribute the 1,000 bills into the
ten envelopes so that some combination of the envelopes will provide any
number (from 1-1000) of bills.
PROBLEM 2 [Not for sissies.]
Early in the last century a man pseudonymed "CALIBAN" wrote a puzzle section in the New Statesman and Nation, a British magazine. Frequent contributors to the column were "Low," "YY", and "Critic." Here is Caliban's Will leaving 10 books to each of the forenamed, selection being made according to the following:
(1) No one who has seen me in a green tie is to choose before Low.
(2) One, at least, of the following is true:
(a) YY was in Oxford in March, 1920.
(b) The first chooser never lent me an umbrella.
(3) One, at least, of the following is true:
(a) Low chooses second.
(b) Critic chooses before the one who first fell in love.
Assume that none of the conditions (1,2,3) is to be superfluous to the heirs. Now Low, YY, and Critic could not remember any of the relevant facts, something Caliban did not know. But the family solicitor pointed out, assuming the problem to be properly constructed (none of the statements (1), (2), or (3) being superfluous to the solution), the order could be inferred. What is the order of choosing?
P.S. If you correctly solved this problem you will
be awarded the Croix de Jer with four burnt marshmallows.
NB: These are not Jer's answers - these are my (Mark's) version of the answers. 1) is trivial but 2) is not and I'm still working on it, though I have the full solution - actually two versions of the full solution - from Jer.
1) For those with exposure to binary notation they will have gotten it immediately.
The bills are distributed as 1, 2, 4, 8, 16, 32, 64, 128, 256, and 489 in the envelopes. Any amount up to 1000 can be constructed from some combination of the envelopes.
2) What a monster! An answer (which I provided Jer), and as it turns out, the correct answer, is: Low, Critic, and YY.
But to receive the Croix de Jer you must be able to demonstrate that this is the only possible answer, which is somewhat harder, and will be explained here once, or if, I finish it, or after about another two weeks. So there. No marshmallows for me yet.
By the way, Jer told me that when the solution was first published, by an eminent British mathematician (I recall), it was claimed that you could also determine who lent Caliban the umbrella.
This caused a huge controversy, for the actual fact
is you cannot determine that from the puzzle as stated. Extra points on
your Croix for demonstrating why that is true.
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