From Newsgroup: rec.puzzles
On 03/12/2025 15:53, David Entwistle wrote:
From '536 Puzzles and Curious Problems' by Henry Ernest Dudeney.
A man went into a bank with a thousand dollars, all in dollar bills, and
ten bags. He said, "Place the money, please, in the bags in such a way
that if I call and ask for a certain number of dollars you can hand me
over one or more bags, giving me the exact amount called for without
opening any of the bags."
How was it to be done? We are, of course, only concerned with a single application, but he may ask for any exact number of dollars from one to
one thousand.
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$1
$2
$4
$8
$16
$32
$64
$128
$256
$489
Proof: the first 9 bags can express any nine-bit integer 0-511.
If he asks for N where N is more than $511, the bank can give him
the $489 bag, and add $(N-489) from the other 9 bags.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within
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