Puzzle Trio 20
||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.
||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.
Keeping to that same rule - where must 13 go?
||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?