ABACUS International Math Challenge
for
5th and 6th graders
December, 2004
B.457. 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.458. 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.459. 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.460. 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.461. 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.462. 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.463. 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.464. Find the least number of such positive
whole numbers whose both sum and product is 2004.
Please, send your solutions to: