GCS 2014-15 October 3rd and 4th

3rd and 4th graders

October, 2014

A.977. A magician pulls out pigeons from his hat. Which of the following statements are true, maybe true, or false, if we know that there are 3 gray, 1 white and 2 colorful pigeons in the hat:

a) if he pull out 4 pigeons, there will be at least one gray among them.
b) if he pull out 3 pigeons, there will be at least one of each kind of pigeon.
c) if he pull out 4 pigeons, there will be at least two pigeons of the same color.
d) if he pull out 6 pigeons, there will be at least two pigeons of each color.
e) if he pull out 5 pigeons, there will be more colorful than gray.
f) if he pull out 5 pigeons, there will be more gray than colorful.

A.978. In a class 14 students collect stamps, 16 collect postcards. 5 students collect both and 4 students collect none of them. How many students are there in this class?

A.979. In the storage of a circus they keep the equipments in 4 boxes: one bigger box and 3 smaller boxes. One worker says that the bigger box is 30 kg heavier than a smaller one. Another worker says that the 3 smaller boxes together are 30 kg heavier than the bigger box. How heavy are the boxes if both workers are correct?

A.980. The clown climbs up the 6-step-ladder step-by step, or sometimes he skips a step. How many different ways can he get up to the top of the ladder?

A.981. The stage master lost his watch. Unfortunately for him, only the clown was nearby, so he had to ask the clown for the exact time. The clown said: "If my watch were 22 minutes late then it would show 11:54, but it is 22 minutes fast." Help the stage master!

A.982. For the evening performance they sold 1000 tickets, which were numbered, starting with 1. Every person who's ticket-number contained the digit 7 received a present. How many presents did they give out that evening?

A.983. For the three bear cubs they make a fence out of 2-meter-long elements. Using 36 elements, they fence around a rectangular-shaped area. How many different dimensions could this area have if they used every element in whole? Which one of these rectangles has the greatest area, and how much is that area?

A.984. The animals love to play on the see-saw in their free time. One lion can balance out 5 monkeys, and one leopard can balance out 4 dogs, and one leopard and 2 dogs can balance out 3 monkeys. How many dogs can balance out one lion?

Please, send your solutions here.

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