1) For any acute angled triangle, how do you construct the inscribed triangle with the shortest perimeter?
2) In the common meaning of the term, when is something statistically significant?
3) In each row, place a three-letter word, which attaches to the end of the word to the left and the beginning of the word to the right making a longer word in each case. The last letter of each three-letter word, when read downwards, makes a new word. What is it?
| ANY | _ _ _ | SELF |
| MATCH | _ _ _ | ROOM |
| FINGER | _ _ _ | TOP |
| OVER | _ _ _ | OWED |
| TAT | _ _ _ | THY |
| MEN | _ _ _ | RID |
| SEE | _ _ _ | ME |
4) You are in the audience of the Mensa game show, and the host calls your lucky number. Loud applause follows you to the stage. There are three doors. Behind one is a candy-coloured Porsche, your dream car. Behind the other two are toaster ovens. You announce your blind choice of door: one, two or three. The host follows by looking behind the other two. He opens one that has a toaster oven for all to see. The host then offers you a chance to change your door selection. The host finally opens the door you’ve selected and you win what’s behind it.
As it happens, you first pick door number one. The host looks behind doors two and three. He opens door three, where you see a toaster oven. He offers you a chance to change your door. Query: do you stay with door one, switch to door two, or does it matter?
Answers to January’s puzzles
1)
| 36 = six times six |
| 20 fingers and toes |
| 21 gun salute |
| 4 right angles in a rectangle |
| 1 partridge in a pear tree |
| 20000 leagues under the sea |
| 2468 who do we appreciate |
| 1969 = first man on the moon |
| 1815 = Battle of Waterloo |
| 1024 = bytes in a kilobyte |
| 206 bones in the human body |
| 81 = # whacks by Lizzie Borden |
| 93 million miles to the sun |
| 1 for the road |
| 0 = freezing point of water |
| 1 armed bandit |
| 40 winks |
| 77 sunset strip |
| 3 score years and ten |
| Life begins at 40 |
| sweet sixteen and never been kissed |
| 8 points on a compass |
| 10 toes on a pair of feet |
| 7 colours of the rainbow |
| 3 nephews of Donald duck (Huey, Dewey, Louis) |
| 5 loaves and three fishes |
| 5 continents on earth |
| 6 of one & half a dozen of another |
| ring around the rosy |
| 8 legs on a spider |
| two thumbs up |
| fortnight = 14 days |
| black and blue |
| 4 chambers in the heart |
| 24 blackbirds baked in a pie |
| on cloud 9 |
| 1000 = square root of a million |
| 1001 Arabian nights |
| 1 foot in the grave |
| Ali Baba and the 40 thieves |
| 21 spots on a die |
| 2 sides to every story |
| 4 seasons in a year |
| 88 keys on a piano |
| 26 miles in a marathon |
| 25 years married = silver wedding anniversary |
| 76 trombones led the big parade |
| 4 weddings and a funeral |
| 1000 words that a picture is worth |
| 1 wheel on a unicycle |
| 8 maids a milking |
| 288 = two times a gross |
2) The square root of two. 3) If the escapee is a truth-believer, neither Pif nor Paf could have asked the question. If the reverse, either could have asked. 4) The answer is x. Go forward three letters, then five, then three, etc.
