Mental Exercise

Linked Rings.  Consider the following three linked rings shown in the illustration. How could all three rings be separated from one another by cutting just one ring?

Family Math.  The Smith family has a number of children with one on the way. If the new child turns out to be a boy, then the family will have an equal number of boys and girls. If the fourth child turns out to be a girl, then the family will have twice as many girls as boys.

Opposites. There are two words, opposite in meaning that both end in the letters ‘st.’ What are the words?

Handshake Counting.  Eight people attended the first meeting of a new social club. Every member introduced themselves and shook hands with every other member. How many total handshakes took place?

Hot donut. If you have a metal torus (a torus is a mathematical shape like a smooth donut) and you heat it to expand the metal, will the hole in the center get larger or smaller in diameter?

Page Sum.  A twenty page tabloid newspaper is printed on five sheets of paper. The sheets are stacked and folded over so that the first two pages and the last two pages belong to one sheet and so on. If you pull one of the sheets at random and sum up the four page numbers on that sheet, what is total?

Four Square.  Look at the following stick figure. Imagine that it is composed of matchsticks. The matchsticks form five squares, can you move just two of the match sticks to form just four equal sized squares? 

Four of Seven.  Two teams contest a seven games tournament to determine a champion. The tournament must go at least four games. At the end of four games what is the most likely outcome: one team wins four games to none, one team is ahead three games to one, or the tournament is tied two games apiece? Assume that each team has an even chance of winning each game.

 Answers

Linked Rings.  This is a bit of a trick question. Actually the three rings have the interesting property that cutting any one of them allows all three to be totally separated.

Family Math.  The family has three girls and two boys.

Opposites.  The words are ‘first’ and ‘last.’

Handshake Counting.  The total number of handshakes equals 7 + 6 + 5 + 4 + 3 + 2 +1 = 28.

Hot donut.  All dimensions of the metal torus, including the diameter of the hole, will expand.

Page Sum.  The first sheet has pages 1, 2, 19, 20. The next sheet has 3, 4, 17, 18. Each sheet totals 42.

Four Square.  The light grey lines indicate where the matchsticks where moved from, bold line where the are moved to.

Four of Seven.  It might be hard to believe, but the most likely outcome is three wins to one. This will occur half the time, 8 out of 16 outcomes: