## 5th and 6th grade, February, 2018

B.1177. Using only 200 and 500 monetary unit bills, what are all those values divisible by 100 that are payable without any change necessary?

B.1178. Kolmogorov, a Russian mathematician once said: “You have to be a very good mathematician just to imagine, with your eyes closed, a plain cross section of a cube where the plain, containing the center of the cube, is perpendicular to one of the diagonals of the solid.” What polygon is this cross section?

B.1179. A clock on the wall bells at every hour and at every half an hour. (Once at the half hours and as many times as the number of hour at the full hours.) One night I woke up for a bell. How much longer do I have to stay awake in order to tell the exact time for sure based on the number of bells only?

B.1180. The opening dance at a ball is a waltz. One of the main attractions of the dance is when the girls change from a billiard formation into a flower formation. The beauty of the move is that during the change only one girl moves at a time by having her skirt roll around the skirt of another girl until her skirt touches her two neighbors’ skirts again. Create a choreography which changes from the billiard formation to the flower formation using four such movements.

B.1181. We have a subscription for a daily newspaper, but our mailbox is not big enough for the newspaper to fit in without folding it. Our mailman, just for his own entertainment, decided that he will fold the newspaper differently every day. He always folds the paper parallel to its shorter side so that the layers cover each other completely. On the diagram below you can see all possible mainly different ways of folding the paper into 3 layers. How many mainly different ways can you fold the paper into 4 layers?

B.1182. Ten players are participating in a ping-pong competition. If you lose 2 matches, you are out. (There is no tie.) In each round they pick the opponents randomly from those who are still in the competition. If somebody does not get an opponent, he advances to the next round without a match. What is the least and what is the most number of matches that can decide the winner of this competition?

B.1183. We roll a prime number with each of three regular dice so that the sum of those primes is a prime, also. What could those 3 numbers be?

B.1184. Let the length of a match be a unit. Using 18 matches, create a polygon with an area of 9 units.

Please send your solutions here.

The Sharma Kamala Educational Trust is sponsoring the participation of students from India. So, if you are a student living in India, please, send your solutions to: Group B from India

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