The next number in the sequence is n squared minus m or f(n,m) = n2 – m f(6,9) = 62 – 9 = 27 f(9,27) = 92 – 27 = 54 f(27,54) = 272 – 54 = 675 f(54,675) = 542 – 675 = 2241
I was visiting a friend one evening and remembered that he had three daughters. I asked him how old they were. “The product of their ages is 72,” he answered. Quizzically, I asked, “Is there anything else you can tell me?” “Yes,” he replied, “the sum of their ages is equal to the number of my house.” I stepped outside to see what the house number was. Upon returning inside, I said to my host, “I’m sorry, but I still can’t figure out their ages.” He responded apologetically, “I’m sorry, I forgot to mention that my oldest daughter likes strawberry shortcake.” With this information, I was able to determine all three of their ages. How old is each daughter?
The house number alone would have identified any of these groups. Since more information was required, we know the sum left the answer unknown. The presence of a single oldest child eliminates “2 6 6”, leaving “3 3 8” as the only possible answer.
Four different-colored balls are being used in a gym class activity – blue, red, yellow and orange. Each student must hold two different-colored balls, but no two students can have the same two colors (for example, only one student can hold the blue and red ball).
Suppose you have twelve eggs and a balance scale. All of the eggs are identical except for one whose only difference is its weight. Using the scale only three times, determine which egg is the odd egg out and whether it is heavier or lighter than the other eggs.
Weigh four against four. If they’re equal, weigh three of them against three you haven’t weighed. If they balance too, weigh the last remaining egg against any of the others to see if it is lighter or heavier. If the three suspects are heavier, weigh one of them against another and the one that goes down is it. If they balance the remaining suspect is heavy. Use the same process if they’re lighter. If the initial four vs four don’t balance, weigh two heavy eggs and a light egg against one heavy egg, one light one and a known normal egg. If they balance weigh the remaining two light eggs against each other. If they balance the unweighed heavy egg is the odd one out. If the side with two heavy eggs goes down weigh them against each other. If they balance it is the light egg on the other side. If the other side goes down it is either because of one heavy egg on that side or because the one light egg on the other side is lighter than the rest. Weigh one of them against a known normal egg to determine which is true.