ABACUS International Math Challenge
for
5th and 6th graders
March, 2005
B.481. Steve, Alex, Leslie, and Kate each
have a favorite car, a favorite type of chocolate, and they each have a
dog. We have the following information about them:
- The owner of Bell loves chocolate with almond.
- Alex is dreaming of a Honda while he is eating milch chocolate.
- Kate takes Caesar for a walk every Sunday.
- The owner of Trixie would love to have a Jaguar.
- Leslie never buys anything but chocolate with yogurt.
What is the name of the owner of Fletcher? Who loves chocolate with
raspberry?
B.482. See the balance on the following
diagram, which shows that every arm of the balance is in equilibrium. (The
horizontal bars are suspended at their midpoints.) Identical shapes have
identical masses. The mass of the square is 1 dkg. What are the masses of
the other shapes?
B.483. Two cities (A and B) are connected
by a straight road. There are 5 other cities on this road between cities
A and B. The distance between any two out of these 7 cities is a whole number
of kilometers. If somebody walks from one city to another, from the number
of kilometers walked you can tell exactly between which two cities the person
walked. City A is 25 km from City B. Give a possible arrangement for the
locations of the 5 other cities between A and B.
B.484. Look at the following interesting
two pairs of products: 12x42 = 21x24; 21x48 = 12x84. Give three more similar
interesting products in which the product does not change when you switch
the digits of the 2-digit factors.
B.485. A 5 cm long snail wanted to climb
out of a dry well using the vertical walls of the well. The snail was rested
and climbed up 10 body lengths in the first minute, 9 body lengths in the
second minute, and so on. After the 10th minute the snail stops to rest
for awhile. After resting a little, it continues to climb the same way as
before. The snail started at the bottom of the well, but half way up it
slipped and slid back down to one quarter of the whole depth. Here it rested
again and then after 10 minutes of climbing the same way, it was still only
at 2/3 of the way up. How deep is this well?
B.486. A 5-digit number E rounded to the
nearest ten thousands is A, rounded to the nearest thousands is B, rounded
to the nearest hundreds is C, rounded to the nearest tens is D. We know
that A<B<C<D<E. How many such 5-digit numbers are there?
B.487. There are 6 different color balls
in a box: red, yellow, green, blue, white, and black. We takes balls out
of the box one at a time without looking until we took the red ball out.
We do not put balls back. How many different ways can we get to the red
ball if the order of the balls taken out does matter?
B.488. Given two piles of stones, one with
13 stones and another with 7 stones. Players alternate turns. On his turn,
a player may remove 1, 2, or 3 stones from either pile. The winner is the
player who removes the last stone of all. (That is, his opponent can't move.)
If both players play well, who will win this game, the first player to move
or the second?
by Austin Sheppard
Please, send your solutions to: