SOLUTIONS
therefore five times as long, 216ft. 8in. A curious feature of the
puzzle is the fact that with the dimensions given the result is exactly
the sum of the height and the circumference.
99.—
The Two Errand Boys.
All that is necessary is to add the two distances at which they
meet to twice their difference. Thus 720 + 400 + 640 = 1760 yards,
or one mile, which is the distance required.
100.—
On the Ramsgate Sands.
Just six different rings may be formed without breaking the
conditions. Here is one way of effecting the arrangements.
ABCDEFGHIJKLM
ACEGIKMBDFHJ L
ADGJMCF ILBEHK
AEIMDHLCGKBFJ
AFKCHME JBGLD I
AGMFLEKDJCIBH
Join the ends and you have the six rings.
101.—
The Three Motor Cars.
The only set of three numbers, of two, three, and five figures
respectively, that will fulfil the required conditions is 27 x 594 =
16,038. These three numbers contain all the nine digits and 0,
without repetition, the first two numbers multiplied together make
the third, and the second is exactly twenty-two times the first. If
the numbers might contain one, four, and five figures respectively,
there would be many correct answers, such as 3 x 5,694= 17,082,
but it is a curious fact that there is only one answer to the problem
as propounded, though it is no easy matter to prove that this is
the case.
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