Cleave Books
Puzzle Trio 20

58. It is possible to use all the whole numbers from 1 to 16 and match them up into eight pairs so that each pair adds up to a square number.
For example, (1, 3) and (2, 14) could both be suitable since they give 4 and 16, both of which are square numbers.
But they do not have to be different square numbers.
List all the eight pairs.

59. The numbers 1 to 12 have been written on four lines as shown.
There is a rule which fixes on which line each number must go.
12


6


10




45


9




3


78













1112
Keeping to that same rule - where must 13 go?

60. Tom has a contract to dig out some foundations and it must be done in 30 days.
His own machine, which he wishes to use as much as possible, would take 48 days to do all the work. He can hire a bigger machine which would do the complete job in 21 days, but it costs 1000 a day.
There is only enough room for one machine at a time.
What is the least number of days for which he will have to hire the larger machine?

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