ABACUS International Math Challenge
for
5th and 6th graders
January, 2003
B.353. Anton and Ben are competing in 50-meter
speed walking. They each walk with a constant speed for the whole race.
If they start at the same point at the same time, Anton beats Ben by 10
meters at the finish line. So now Anton start from 10 meters behind the
starting line giving Ben a handicap. If they start at the same time, and
they both walk by the same speed as they did in the previous race, who wins
the race this time and by how much distance?
B.354. A spiral is given with its center
point X. As you walk on the spiral, you continually get farther away from
its center point. The spiral never ends. The picture shows only the beginning
of it. Now you draw a circle with the same center point. How many mutual
points do the two lines have?
B.355. You have two circular discs with
a radius of 9 cm each. You want to cover a 10-cm radius circular disc with
them completely. How many different ways can you do it?
B.356. Tom's father loves chocolate balls.
You can buy them in 3 different bags: one contains 6, the other contains
9, and the third kind contains 20 chocolate balls. You may not open the
bags before you buy them. Tom wants to surprise his father on his birthday
by buying as many chocolate balls as many years old his father is. Unfortunately,
Tom cannot do it this year, but starting next year he will be able to do
it every year. How old is Tom's father this year?
B.357. Out of 40 shoppers, 12 of them liked
the apples, 23 liked the oranges, and twice as many did not like either
as many liked both. How many shoppers liked both?
B.358. If you read a two-digit number backwards,
you get a 4.5 times greater number. Find this number.
B.359. In a group of people the ratio of
the number of women and the number of men is 11:10. The average age of the
women is 34, and the average age of the men is 32. What is the average age
of the group exactly?
B.360. You have a lot of 1 
volume cubes.
Build a column with a 2cm x 2cm base. How tall is the column if its surface
area is 2000 
?
Please, send your solutions to: