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.