ABACUS International Math Challenge
for
7th and 8th graders
March, 2000
C.177. Find a six-digit number in which
the digits will rotate when the number is multiplied by either two, three,
four, five or six.
by Christian Kiss-Toth, Hungary
C.178. At a target shooting place the targets
have 4 concentrical circles with radiuses 1, 2, 3, and 4 units. Every shot
costs $4. If you hit the inner circle you get $10, for hitting the smallest
ring you get $7, for the next ring you get $3, and for the biggest ring
you get $1. Is it worth it to shoot if we suppose that you always hit the
target, but you have an equal chance to hit any point on it?
C.179. A party of 5 couples has to be divided
into 2 groups so that one of the groups must contain 6 people and among
them at least 2 couples. How many different ways can this be done?
C.180. Can you place a series of circles
in a unit-area rectangle so that the circles do not intercept each other,
none of the circles is contained inside of another circle, and the sum of
the radiuses of the circles is 2000?
C.181. Divide the circumference of a circle
into equally long arcs with 11 points. How many such triangles can you draw
using these points as vertices, that contain the center of the circle inside
of them?
C.182. A bird trader sold 10 bird cages
with a bird in each, but the buyers usually wanted to buy a different cage
for the bird of their choice than the one the bird was actually in. The
trader, for safety reasons, switched the cages in such a way that he used
an extra, empty cage and he always moved only one bird into an empty cage.
At most, how many such moves do you need to satisfy all 10 costumers, even
in the worst case scenario?
C.183. In the following
multiplication same letters mean the same digits, different letters mean
different digits. What could the value of the product be?
BAG * BAG * BAG = HEAVYBAG
by Martin Hablicsek,
Hungary
C.184. We have the following information
about a one-story apartment:
a) There is maximum one door between any two rooms.
b) There is maximum one door from any room to the outside.
c) There are 12 doors in the apartment.
At least how many rooms are there in the apartment?
Please, send your solutions to: