## 7th and 8th Grade, December, 2017

C.1161. What is the least number of steps by which you can change the order of the following number sequence so that the numbers are in a decreasing order from left to right? In each step, you can switch two neighboring numbers.

9; 7; 5; 10; 8; 4; 3; 6; 1; 2

C.1162. In a clothing store 40% of the merchandise is skirts. There are half as many pants as sweaters. There are no other kinds of items in the store. 80% of all the items are for women. The store has the same number of pants for women as sweaters for women. What percent of all the items are men’s pants? (Assume all skirts are for women.)

C.1163. The diagram below shows the sketch of a train station with one main line. How many different ways can a train coming from the left go through this station?

C.1164. How many different ways can you take the shortest path from c5 to h2 with a King on a chessboard?

C.1165. Fill up a cube of edges 12-cm each, 5/8 of the way with water, then tilt it about one edge. The diagram below shows a cross section of the cube with the horizontal line representing the water level in it. You know that LC is twice as long as KB. How long is LC?

C.1166. Olga has 5 different rings, each of which can fit on her ring finger, as well as her middle finger. She always wears 2 rings on her ring finger and 3 rings on her middle finger, but only on her left hand. How many different ways can she wear these rings?

C.1167. As you can see below, I drew two squares in a 30 cm x 30 cm square. How much is the difference in the areas of squares A and B?

C.1168. The last time Uncle Tom went to the theater, he noticed the following: even when his wife was wearing 10 cm high heels, she was 2 cm shorter than him; Uncle Tom himself, when wearing his 33-cm tall cylinder hat, is 1 meter taller than their daughter, Dorca. How tall are the members of this family if the mother and daughter together (without the high heels and the cylinder hat) are 1 meter taller than Uncle Tom?