## 5th and 6th Grade, November, 2017

B.1153. You can button up a shirt correctly only one way. Joe sometimes gets in a hurry when he buttons up his shirt with 6 buttons. He starts with any button and misses the correct buttonhole by one location. He then buttons all the rest without skipping any buttonholes. How many different ways can Joe button his shirt?

B.1154. Erase five digits from the number 5,109,324,169 so that the remaining five-digit number is as small as possible. What number do you get?

B.1155. Some students of a 6th grade class with 35 students went to see a movie. Aron and Lilly were there, also. Aron noticed that 4 times as many girls as boys (not counting himself) from his class were there. Lilly, on the other hand, noticed that 3 times as many girls (not counting herself) as boys from her class were there. How many girls and how many boys were at the movie?

B.1156. Ashia typed up a 6-digit number on her computer, but the key for the digit 3 (which she needed twice) did not work on her keyboard. So the number that appeared on her screen was only 2017. How many different numbers could Ashia have typed?

B.1157. The king keeps 1, 2, 3, …, 18 golden coins in 18 identical silver boxes respectively. He gives all of them to his 3 sons as a present. Is it possible to divide this present fairly among the sons? Help the princes in this task, if you know that you cannot change the number of coins in any of the boxes. (The silver boxes are valuable also, but you do not know how many golden coins they are worth.)

B.1158. By the diagonals of the squares, we draw the following figure on a square grid. What is the area of the light part, if the area of the dark part is 285 sq.cm?

B.1159. In a jar the number of bacteria triples every 20 seconds. Three minutes from now the number of bacteria in the jar will be between 260,000 and 290,000. How many bacteria are there in the jar now?

B.1160. There are 6 different aged men sitting at a table. Every one of them is older than 10 years, none of them has a digit zero in his age. The sum of their ages is 263 years. You know that everybody’s age has two things in common: it is a two-digit number, and one of the digits in it is 5 more than the other. How old are they each?