5th and 6th graders
January 2015
B.1001. How many sets of two square numbers with the difference of 20152 are there?
B.1002. In a family three boys have at least one younger sibling and two boys have at least one older sibling. Two girls have at least one older sibling and one girl has at least one younger sibling. There are no twins in this family. How many children are there in this family, and in which order could the boys and girls be born?
B.1003. Timea is putting her building blocks on her two-arm balance. (Blocks with different colors have different weights.) First she puts a red and a blue on one side and a green and a yellow on the other side, and they are in balance. Then she switches the blue and the green, and this way the yellow and the blue together are heavier than the red and the green. Finally, she finds that the green and the blue together are heavier than the red and the yellow. What color block is the heaviest?
B.1004. On each bank of a river stands King Arthur and Sir Robin. Both of them has a lock with a matching key, but the two locks and their keys are different. One of the men has a box with two pairs of metal bands on it which can be locked by one lock on each pair of bands. (Of course, you can lock to box by using only one of the two pairs, also.) King Arthur wants to send some gold coins to Sir Robin. There is a carrier on the river who transports everything but people, but he steals everything that is not locked (even an open empty box). Could the king still send the gold to Sir Robin? (Notice that the box could be with either one of the two men originally.)
B.1005. The vertices of the gray rhombuses are the midpoints of the sides of the square and the sixths points of the diagonals of the square. How big is the gray area if the side of the square is 21 cm?
B.1006. Let the letters of the word ABACUS mean number digits. (Same letters mean the same digit.) Therefore, the word means a 6-digit number. What number is it if you know that:
A+B+C=18
AxCxU=48
SxUxB=378
B.1007. Numbers that are the same when read backwards are called palindrome numbers. Find all those palindrome numbers between 10 and 1000 in which the sum of the digits is the same as the product of the digits.
B.1008. You have four perfect dice, and you roll them all at once. How many different ways can the sum of the numbers rolled be 20? (Two rolls are identical if you get the same four numbers.)
Back to Abacus
Back to 2014-15 Problems
Please, send your solutions here.
Back to Abacus
Back to 2014-15 Problems
Junior Kindergarten – Grade 8 86 Fourth Ave. New York, NY 10003 (212) 475-5609 | Grades 9 – 12 46 Cooper Square New York, NY 10003 (212) 475-5610
Grace Church School is a co-educational independent school in downtown Manhattan, New York City
providing instruction for over 700 students in Junior Kindergarten through Grade 12.
providing instruction for over 700 students in Junior Kindergarten through Grade 12.
Grace Church School © 2021