Neurobics

Russell Dear

The Conference Dinner

"There are 72 delegates coming to the dinner," the conference organiser commentated. "How will you seat them?"

"Only delegates from New Zealand, Australia and Fiji are attending so I thought I'd sit them three to a table," the social secretary replied.

"Good idea," said the conference organiser. "You'll want to mix the nationalities as much as possible at each table."

"Yes," replied the social secretary. "I'm still working on the seating plan but I've already noticed that no matter how I divide the 72 delegates, at least one at each table is a New Zealander."

Exactly how many New Zealanders, Australians and Fijians are attending the conference dinner?

What a Mix-up

Colin reckoned he was a bit of a painter, a house painter that is, and was decorating his house after work. He needed six litres of light grey paint for the roof which his wife Alice had told him to mix as two parts white to one part black. Sometimes though, Colin's left hand didn't know what his right hand was doing, and today was such an occasion. While his left hand was mixing two litres of white paint his right hand was mixing four litres of black.

"Oh dear", mused Alice, "I asked him to mix me a light grey paint and he's mixed me a dark grey one instead".

What is Colin to do? He could throw away all the dark grey paint and begin again. On the other hand, he could add six litres of white to the mixture and then throw half of that away, again wasting six litres. What should he do so as to waste as little paint as possible?

Minding the Kiddies

One afternoon Don's wife asked him to entertain the grandchildren while she went shopping for some party goodies. First they all paired off to play a few games of noughts and crosses. Sally, Don's opponent, quickly learned how to force a draw and soon got bored. Don then decided to teach the children poker. They weren't that keen at first but when Don provided twenty dollar coins for stake money they played happily until Granny returned.

At the end of the game all the grandchildren had some coins left. In fact the product of the number of coins each child had was the largest possible multiple of 100 it could be. How many grandchildren did Don entertain?

Russell Dear is a Mathematician living in Invercargill