ABACUS International Math Challenge
for
5th and 6th graders
September, 2004
B.433. In the final round of the diving
competition of the Olympics the athletes A, B, C, D, E, and F, took their
final dives in this order. There was a scoreboard that showed, after each
dive, the actual place of the diver, who just went, out of those who already
took their last dives. The spectators saw two first place, and four third
place written on the scoreboard. What was the final order of these athletes?
B.434. There is an expedition in the desert
Sahara. There are people, horses and two-humped camels in the expedition.
There are three times as many humps as horses. Every horse and every camel
has a rider, and 5 people, which is a third of the number of camels, are
walking. How many feet are walking in the sand of the desert?
B.435. You have 10 boxes and 44 balls.
Can you place a total of 44 balls into 10 boxes so that every box has a
different number of balls in it. (You may not put a box into another box.
every box is big enough to hold even all the balls.)
B.436. Find all those 5-digit numbers in
which every digit is greater than the sum of the digits placed to the right
of it in the number.
B.437. Leslie had his birthday. His parents
brought a cake for him, but during the party the cake disappeared. Leslie
asked those of his friends whom, in his opinion might have hid the cake,
and then he voiced his opinion, also. Here are the answers:
Ben: "It was Joe."
Joe: " Andrew is lying."
Ivan: "It was Elton."
George: "It wasn't Ivan."
Andrew: "It wasn't me."
Elton: "Ben says the truth."
Frank: "It was me."
Leslie: "It was Ben."
Who did it, if only one out of the 8 statements is true, and there was
only one person who did it?
B.438. You divide each side of a cube into
4 identical squares. (This way you get 24 identical squares.) You color
them using red, blue and green paint so that every 2 squares with a mutual
side are different colors. How many red, blue, and green squares do you
have?
B.439. You have several cubes with a total
volume of 2004 cubic cm. The edges of the cubes measured in cm are whole
numbers. What is the minimum, and the maximum number of such cubes?
by Zsuzsa Bognár, Hungary
B.440. Timea wrote a few numbers on a piece
of paper. She realized that the product of each number with itself is written
on the paper, also. Which numbers did she write on the paper?
Please, send your solutions to: