ABACUS International Math Challenge
for
5th and 6th graders
December, 2006
B.561. How many 3-digit even numbers do
you know of in which the digit in the hundreds place is the sum of the digits
in the tens and the ones place?
B.562. Andy, Ben and Clifton are playing
cards. In every game there is only one loser. At the end of each game the
loser has to give all his money to the other two guys evenly. After three
games the scoreboard is as follows: everybody lost once, Andy has $40, Ben
has $100 and Clifton has no money. Who lost the first game?
B.563. There are 13 different triangles
in which the length of every side measured in centimeters is a whole number,
and none of the sides is longer than a given length, which is a whole number
of centimeters. How long is this length?
B.564. In a gift shop you can buy candles
in different shapes and packages for the holidays. The price of each packages
is the sum of the prices of the candles in it. (Candles of the same shape
have the same price.) The prices of the packages from left to right are
$21, $19, and $24. How much does the fourth package cost?
B.565. We write all the whole numbers from
1 to 9 into the circles on the following diagram so that the sum of the
numbers on each side of the triangle is the same. What is the difference
between the smallest and the greatest such sums?
B.566. Find the smallest positive whole
number that gives you a total remainder of 42 when divided by 13, 15 and
17.
B.567. Find all those positive whole numbers,
which are 33 times more than the sum of their digits.
B.568. Find the smallest positive whole
number that is divisible by 5 and the sum of its digits is 99.