GCS 2014-15 September 5th and 6th

5th and 6th graders

September, 2014

B.969. In the final round of the diving competition of the Olympics the athletes A, B, C, D, E, and F, took their final dives in this order. There was a scoreboard that showed, after each dive, the actual place of the diver, who just went, out of those who already took their last dives. The spectators saw two first place, and four third place written on the scoreboard. What was the final order of these athletes?

B.970. There is an expedition in the desert Sahara. There are people, horses and two-humped camels in the expedition. There are three times as many humps as horses. Every horse and every camel has a rider, and 5 people, which is a third of the number of camels, are walking. How many feet are walking in the sand of the desert?

B.971. You have 10 boxes and 44 balls. Can you place a total of 44 balls into 10 boxes so that every box has a different number of balls in it. (You may not put a box into another box. Every box is big enough to hold even all the balls.)

B.972. Find all those 5-digit numbers in which every digit is greater than the sum of the digits placed to the right of it in the number.

B.973. Leslie had his birthday. His parents brought a cake for him, but during the party the cake disappeared. Leslie asked those of his friends whom, in his opinion might have hid the cake, and then he voiced his opinion, also. Here are the answers:

Ben: "It was Joe."

Joe: " Andrew is lying."

Ivan: "It was Elton."

George: "It wasn't Ivan."

Andrew: "It wasn't me."

Elton: "Ben says the truth."

Frank: "It was me."

Leslie: "It was Ben."

Who did it, if only one out of the 8 statements is true, and there was only one person who did it?

B.974. You divide each side of a cube into 4 identical squares. (This way you get 24 identical squares.) You color them using red, blue and green paint so that every 2 squares with a mutual side are different colors. How many red, blue, and green squares do you have?

B.975. You have several cubes with a total volume of 2014 cubic cm. The edges of the cubes measured in cm are whole numbers. What is the minimum, and the maximum number of such cubes?

B.976. Timea wrote a few numbers on a piece of paper. She realized that the product of each number with itself is written on the paper, also. At most, how many numbers did she write down? In this case, which numbers did she write on the paper?

5th and 6th graders

September, 2014

Please, send your solutions here.