5th and 6th graders

December 2014

 
B.993. Divide 11 identical pizzas between 15 hungry children so that everybody would get an equal amount of pizza, but you would not cut any of the pizzas into more than 14 pieces.

B.994. Find all those 6-digit numbers in which the first digit is divisible by 1, the second digit is divisible by 2, the third digit is divisible by 3, the fourth digit is divisible by 4, the fifth digit is divisible by 5, and the sixth digit is divisible by 6, both if you read the number from left to right or from right to left.

B.995. You can read the time on a digital clock every day from 00:00 to 23:59. Let's call the AB:AB and the AB:BA minutes (A and B are not necessarily different digits) "beautiful minutes". How many "beautiful minutes" are there in a day?

B.996. You have 3 identical rectangular-based columns with edges starting from the same vertex being 1, 2, and 3 cm long. Using all three of them, you may build different solids by gluing identical sides to each other. Then you paint the surfaces of these solids. How do you have to glue them together if you want to use the least amount of paint? Can you build a solid with a surface area of 52 square cm?

B.997. You want to cover the floor shown on the diagram with tiles. How many tiles do you need if you can cover 1 square meter with 27 tiles? You may cut the originally identical tiles every which way you want to.
B.998. There are a few pencils on Kathryn's and Carl's desks. There are 29 more pencils on one desk than on the other, but the number of pencils on both desks is a prime number. Kathryn and Carl share a room, and they would like to put the pencils in boxes so that every box has the same number of pencils in them. How many pencils can be in a box?

B.999. Find all those 5-digit numbers in which the digits are different, the first digit is divisible by 1, the second digit is divisible by 2, the third digit is divisible by 3, the fourth digit is divisible by 4, and the fifth digit is divisible by 5, both if you read the number from left to right or from right to left.

B.1000. Find the least number of such positive whole numbers whose both sum and product is 2014.

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.
Grace Church School © 2021