Question: A fast food restaurant sells chicken in orders of 6, 9, and 20.
What is the largest number of pieces of chicken you cannot order from this restaurant?
After 6 all numbers divisible by 3 can be ordered (because they can all be expressed as a sum of 6's and 9's). After 26, all numbers divisible by three when subtracted by 20 can be obtained. After 46, all numbers divisible by three when subtracted by 40 can be obtained. After 46, all numbers fit into one of these 3 categories, so all numbers can be obtained. 43 is the last number that doesn't fall into one of these categories (44 = 20 + 6 * 4, 45 = 6 * 6 + 9).
Question: Sum Sam and Product Pete are in class when their teacher gives Sam the Sum of two numbers and Pete the product of the same two numbers (these numbers are greater than or equal to 2). They must figure out the two numbers.
Sam: I don't know what the numbers are Pete.
Pete: I knew you didn't know the numbers... But neither do I.
Sam: In that case, I do know the numbers.
What are the numbers?
Answer: The numbers are 3 and 4.
Since Sam knows the sum of the numbers (x + y) he would only know the answer immediately if the sum was 4 (2 + 2) or 5 (3 + 2). Then when Pete (who knows x*y) knew that Sam didn't know the answer the product must have several numbers that add up to the sum (7 = 3 + 4, 7 = 5 + 2). When Pete doesn't know the answer at this point we know the product must have more than one pair of viable factors (12 = 3 * 4, 12 = 6 * 2). At this point Sam knows the numbers are 3 and 4 because they are the only numbers that meet these criteria.
By David Pleacher
Question: Does a pound of gold or a pound of feathers weight more?
Answer: The feathers. A pound of feathers is measured in avoirdupois weight, in which one pound equals 16 ounces. Precious metals are measured in troy weight, in which one pound equals 12 ounces.
However, the ounces are not measured in the same way. In avoirdupois weight, one ounce = 437.5 grains. In troy weight, one ounce = 480 grains.
So, one pound of feathers weighs (16)x(437.5 grains) = 7,000 grains. One pound of gold weighs (12)x(480 grains) = 5,760 grains.
Question: Jack is taking a tour through a museum's American Presidents exhibit. The person leading the tour tells him "We have a picture of each presidency. Currently Barack Obama is the 43rd person to hold the office." But Jack quickly realizes that there are 44 pictures on the wall. But while walking through the exhibit he realizes why this is.
Why is there one too many photos?
Answer: One president served non-consecutive terms (there was a president between his terms) so he held two different presidencies. The president who really did this was Grover Cleveland.
Question: Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.
What three questions can you ask?
Answer: A possible solution is:
Q1: Ask god B, "If I asked you 'Is A Random?', would you say ja?". If B answers ja, either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is indeed Random. Either way, C is not Random. If B answers da, either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is not Random. Either way, you know the identity of a god who is not Random.
Q2: Go to the god who was identified as not being Random by the previous question (either A or C), and ask him: "If I asked you 'Are you False?', would you say ja?". Since he is not Random, an answer of da indicates that he is True and an answer of ja indicates that he is False.
Q3: Ask the same god the question: "If I asked you 'Is B Random?', would you say ja?". If the answer is ja, B is Random; if the answer is da, the god you have not yet spoken to is Random. The remaining god can be identified by elimination.
For more information about the answer visit the following Wikipedia page.
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