GCS 2013-14 March 7th and 8th

7th and 8th graders

March, 2014

Please, send your solutions in by April 30, 2014.

C.961. The perimeter of a rhombus is 24 cm, its area is 18 sq.cm. How big are its angles?

C.962. Find the smallest 3-digit prime number with all different but only prime digits.

C.963. On a digital clock you can see the time from 00:00 to 23:59. In a day, what is the total amount of time while you can see 3 identical digits on the clock?

C.964. Could the product of 13 consecutive positive whole numbers be

645 127 398 020 820?

C.965. Find 5 square numbers using every positive digit only once.

C.966. There are 1000 points on a plane. We know that at least 3 out of any 4 points are on the same straight line. Prove that all of them or all but one of them are on the same straight line.

C.967. How big are the angles of an isosceles triangle if it has an angle bisector that divides the triangle into two isosceles triangles?

C.968. Two kids are playing cards. There are 32 cards in the deck, and every card has its pair. At the beginning every player gets 5 cards, and then they take one card at a time from the rest of the deck. When the deck is gone they take a card from each other, alternating. If you have a pair (or two pairs), you must put it (them) on the table in front of you. Prove that at the end of the game each player has the same number of pairs.

Please, send your solutions here.

2013-14 Problems

7th and 8th graders

March, 2014

Please, send your solutions in by April 30, 2014.