ABACUS International Math Challenge
for
5th and 6th graders
January, 2008
B.617. You can button up a shirt correctly
only one way. It happens sometimes that you make a mistake and miss a buttonhole.
How many different ways can you do this, if you go from top to bottom on
your shirt with 6 buttons, and after you missed one buttonhole by one buttonhole,
you continue correctly for the rest of the way down?
B.618. Erase five digits from the number
5,109,324,169 so that the remaining five-digit number is as small as possible.
What number do you get?
B.619. Some students of a 6th grade class
with 35 students went to see a movie. Aron and Lilly were there, also. Aron
noticed that 4 times as many girls as boys (not counting himself) from his
class were there. Lilly, on the other hand, noticed that 3 times as many
girls (not counting herself) as boys from her class were there. How many
girls and how many boys were at the movie?
B.620. Cathy typed up a 6-digit number
on her computer, but the key for the digit 1 (which she needed twice) did
not work on her keyboard. So the number that appeared on her screen was
only 2008. How many different numbers could Cathy type up?
B.621. The king keeps 1, 2, 3, ..., 18
golden coins in 18 identical silver boxes respectively. He gives all of
them to his 3 sons as a present. Is it possible to divide this present fairly
among the sons? Help the princes in this task, if you know that you cannot
change the number of coins in any of the boxes. (The silver boxes are valuable
also, but you do not know how many golden coins they are worth.
B.622. By the diagonals of the squares,
we draw the following figure on a square grid. What is the area of the light
part, if the area of the dark part is 285 sq.cm?
B.623. In a jar the number of bacterias
triple every 20 seconds. 3 minutes from the initial moment the number of
bacteria in the jar is between 260,000 and 290,000. How many bacteria were
there in the jar at the initial moment?
B.624. There are 6 different aged men sitting
at a table. Every one of them is older than 10 years, none of them has a
digit zero in his age. The sum of their ages is 263 years. You know that
everybody's age has two things in common: it is a two-digit number, and
one of the digits in it is 5 more than the other. How old are they each?