Question: What is the next number in the sequence? 1 11 21 1211 111221 312211
Answer: The next number it: 13112221. Each number describes the previous number. Starting with 1, the second line describes it 11 (one 1). Then the third line describes 11 as 21 (two 1's). Then the fourth line describes 21 as 1211 (one 2, one 1). This is the pattern.
Question: You create your own Where's Waldo game on a piece of paper. You want your friend to find Waldo but they think you might be pulling a prank on them by not putting Waldo on the paper at all.
How can you prove to your friend that Waldo is on the paper without ruining it for them?
Answer: Cut a small hole in a piece of paper that is just large enough to see Waldo. This way you don't reveal anything about where he is, just that he is there.
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.
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