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#191 Sharing is scaring

Set by Brian Hobbs

It is that time of year again, when the children of Shady Hollows prowl their neighbourhood threatening tricks and receiving treats.

After an evening destined to send shivers down the spine of the local dentist, four friends sit around a table comparing their haul of sugar drops. Suddenly possessed by a spirit of generosity, they each decide to give half of what they have to the friend sitting to their right (anticlockwise).

After this, each child now has more than they started with, except for one. The picture above would have shown what each child ended up with, but Ben and Cindy鈥檚 sweet tooth got the better of them. How many sugar drops did Ben and Cindy each eat? Their dentist is dying to know.

Solution next week

#190 All square

Solution

1-6 6-4 6-4 (giving the number 166464, which is 4082). Square numbers all end in 1, 4, 6, 9, 25 or 00, but ?9/25/00 aren鈥檛 tennis set scores, so the last set was 6-1, 6-4, or ?-6.

If the winner won the first set, possible scores are limited to just two ranges, 606760 to 646776, and 750660 to 766776 (squares of numbers between 775 and 875). If the loser won the first set, the number is a six-digit square that begins 16, 26, 36, 46, 57 or 67.

The only square numbers with the right format for tennis sets are 166464, 633616 and 646416, but 633616 breaks the rule about the winner鈥檚 games being given first, while 646416 wouldn鈥檛 go to a third set.