1) Take two packs of cards. Shuffle each separately. Draw a card from the first pack and shuffle it with pack #2. Look at the top card of pack #1. If this is the queen of spades, what are the odds that pack 2’s top card is the king of spades? Ans: As one card in pack 1 is the queen of spades, the odds that a king of spades was transferred to pack #2 is 1/51. The odds that the top card in pack 2 is a king of spades is therefore the sum of two probabilities: first, the probability that the shifted card was a king of spades and the top card in pack 2 is one of the two kings of spades in pack two (1/51 times 2/53), and second, the probability that the shifted card wasn’t the king of spades (50/51) and pack 2’s top card is that pack’s only king of spades (1/53). The result is the sum of (2/53 x 1/51) and (50/51 x 1/53) which is 52/2703, ie a bit greater than 1/52.
2) The guiltiest of three criminals will face death. While the Judges ponder and the days pass, criminal A asks a guard what’s going on. The guard replies, correctly, that the Judges haven’t considered A’s degree of guilt at all and that criminal B won’t be found worst. What are the odds that A will be executed? Ans: There are six possibilities of relative guilt among A, B and C: ABC, ACB, BAC, BCA, CAB, and CBA. The guard’s reply eliminates all but ACB, CAB and CBA. A is the most guilty in only one scenario, therefore his odds of execution are one in three.
3) My grandfather’s village contained a Mr Carpenter, a Mr Machinist and a Mr Smith. One was a carpenter, one a machinist, and the third a smith, but naturally none followed the vocation indicated by his name. Each was assisted by the son of one of the others, but no son followed the trade corresponding to his name. Mr Machinist wasn’t a carpenter. What was the occupation of Mr Smith’s son? Ans: If Mr Machinist isn’t a machinist or carpenter, he must be a smith. Mr Carpenter is a machinist, and Mr Smith a carpenter. Smith Junior doesn’t assist his father or the smith. He must therefore be a machinist, helping Mr Carpenter.
4) With summer approaching, consider last year’s confusion. Mom had three daughters: Anne, Barbara and Connie. One yachted at Newport, one passed the summer at Bar Harbor, and the third enjoyed Woodstock. One played tennis, one (of course) yachted, and the third played golf. Anne wasn’t at Newport. Connie wasn’t at Bar Harbor, and whichever daughter played golf wasn’t at Woodstock. Connie didn’t go yachting. So who played golf and where? Ans: Let’s see. The girl at Newport went yachting, and Anne wasn’t at Newport. Since Connie didn’t go yachting, it follows that Barbara was on the boat at Newport. If Connie wasn’t at Bar Harbor, Anne must have been. Therefore Connie was at Woodstock and wasn’t playing golf. So Anne played golf at Bar Harbor.
AnswersToMayQuiz: 1) Destructive Obsession. 2) 17.5 days. The worm advances one foot per day. So at the start of the eighteenth day, the worm has progressed 17 feet. During the next twelve hours, the worm advances three feet, which puts it at the top 17 days and 12 hours into the climb. (ed: should we have expected the worm to turn?) 3) 123 – 45 – 67 + 89 = 100. 4) If R is the original number of red cards in portion A, 2R is the number of black cards. Portion B therefore originally consists of 26-R red cards, or 25-R red cards after the shift. The number of black cards in portion B is 26-2R. After the shift, the ratio of red cards to black in portion B is 2 to 1, so
(25-R) = 2
(26-2R) 1
R is therefore 9, which means originally there were 27 cards in portion A (nine red and eighteen black) and 25 in portion B (seventeen red and eight black).
