logic questions attribute All the items in the first list share a particular attribute. The second list is of some items lacking the attribute. Set#1 with: battery, key, yeast, bookmark w/out: stapler, match, Rubik's cube, pill bottle Set#2 with: Rubik's cube, chess set, electrical wiring, compass needle w/out: clock, rope, tic-tac-toe, pencil sharpener Set#3: with: koosh, small intestine, Yorkshire Terrier, Christmas Tree w/out: toothbrush, oak chair, soccer ball, icicle Points to realize: 1. There may be exceptions to any item on the list, for instance a particular clock may share the properties of the 'with' list of problem two, BUT MOST ORDINARY clocks do not. All the properties apply the vast majority of the the items mentioned. Extraordinary exceptions should be ignored. 2. Pay the most attention to the 'with' list. The 'without' list is only present to eliminate various 'stupid' answers. _________________________________________________________________ camel An Arab sheikh tells his two sons to race their camels to a distant city to see who will inherit his fortune. The one whose camel is slower will win. The brothers, after wandering aimlessly for days, ask a wise man for advise. After hearing the advice they jump on the camels and race as fast as they can to the city. What does the wise man say? Solution _________________________________________________________________ chain What is the least number of links you can cut in a chain of 21 links to be able to give someone all possible number of links up to 21? Solution _________________________________________________________________ elimination 97 baseball teams participate in an annual state tournament. The way the champion is chosen for this tournament is by the same old elimination schedule. That is, the 97 teams are to be divided into pairs, and the two teams of each pair play against each other. After a team is eliminated from each pair, the winners would be again divided into pairs, etc. How many games must be played to determine a champion? Solution _________________________________________________________________ flip How can a toss be called over the phone (without requiring trust)? Solution _________________________________________________________________ hundred A sheet of paper has statements numbered from 1 to 100. Statement n says "exactly n of the statements on this sheet are false." Which statements are true and which are false? What if we replace "exactly" by "at least"? Solution _________________________________________________________________ inverter Can a digital logic circuit with two inverters invert N independent inputs? The circuit may contain any number of AND or OR gates. Solution _________________________________________________________________ locks.and.boxes You want to send a valuable object to a friend. You have a box which is more than large enough to contain the object. You have several locks with keys. The box has a locking ring which is more than large enough to have a lock attached. But your friend does not have the key to any lock that you have. How do you do it? Note that you cannot send a key in an unlocked box, since it might be copied. Solution _________________________________________________________________ min.max In a rectangular array of people, which will be taller, the tallest of the shortest people in each column, or the shortest of the tallest people in each r ow? Solution _________________________________________________________________ mixing Start with a half cup of tea and a half cup of coffee. Take one tablespoon of the tea and mix it in with the coffee. Take one tablespoon of this mixture and mix it back in with the tea. Which of the two cups contains more of its original contents? Solution _________________________________________________________________ monty.52 Monty and Waldo play a game with N closed boxes. Monty hides a dollar in one box; the others are empty. Monty opens the empty boxes one by one. When there are only two boxes left Waldo opens either box; he wins if it contains the dollar. Prior to each of the N-2 box openings Waldo chooses one box and locks it, preventing Monty from opening it next. That box is then unlocked and cannot be so locked twice in a row. What are the optimal strategies for Monty and Waldo and what is the fair price for Waldo to pay to play the game? Solution _________________________________________________________________ number Mr. S. and Mr. P. are both perfect logicians, being able to correctly deduce any truth from any set of axioms. Two integers (not necessarily unique) are somehow chosen such that each is within some specified range. Mr. S. is given the sum of these two integers; Mr. P. is given the product of these two integers. After receiving these numbers, the two logicians do not have any communication at all except the following dialogue: <<1>> Mr. P.: I do not know the two numbers. <<2>> Mr. S.: I knew that you didn't know the two numbers. <<3>> Mr. P.: Now I know the two numbers. <<4>> Mr. S.: Now I know the two numbers. Given that the above statements are absolutely truthful, what are the two numbers? Solution _________________________________________________________________ riddle Who makes it, has no need of it. Who buys it, has no use for it. Who uses it can neither see nor feel it.