快猫短视频

#138 Ice cream coincidence

Mr Slippy owns two ice cream vans. His staff check the temperature of the freezers every hour to make sure nothing melts. One day, the freezer in Van A is at -13掳C at 1pm and -18掳C at 2pm. Meanwhile, Van B鈥檚 driver logs the temperatures as -12掳C at 1pm and -20掳C at 2pm.

Mr Slippy is certain that there must have been a time when both freezers were at exactly the same temperature but his drivers say it isn鈥檛 possible to know for sure. Who is right?

#137 Tricky treaty

Solution

James gained one piece of candy in the deal. There are two ways in which the four children鈥檚 piles of sweets could have differences in size of one through to six: (X, X, _, _, X, _, X), or the mirror image (X, _, X, _, _, X, X). For example, if the child with fewest got three pieces, the two ways would be (3, 4, 7 and 9 pieces) or (3, 5, 8 and 9 pieces).

When taking them into one pile and dividing that into four, the first way will result in a remainder of three sweets, the second in a remainder of one. Since I took three pieces and divided evenly, we can deduce that it was the first way. We know that James had one more than another child, so he had the second smallest amount, and when the pieces are averaged out, he gains one piece.