ABACUS International Math Competition
for
7th and 8th graders
September, 1997
C.1. In the following multiplication the same
letters mean the same digits and different letters mean different digits:
.
What number is PETI?
C.2. Use parentheses in the expression
2:3:4:5:6=5 so that it would become a true equality.
C.3. Find 3 different whole numbers so
that any one of them would be a divisor of the number that is one more than
the product of the two other numbers.
C.4. Can you make a payment of $1,000 using
a total of 40 $1, $10 and $100 bills? (You have to use at least one of each
bill.)
C.5. 5 out of 11 coins are false. The mass
of a false coin is 1 gram more or less than the mass of a real coin. Pick
a coin. With one measurement, using a 2-armed balance and measuring weights,
can you decide if this coin is real or false?
C.6. What is the greatest two-digit divisor
of 22227777?
C.7. Prove, that for any whole number n,
either 
is divisible by 10.
C.8. 8 cities are located on the side of
a straight road in the following order: A, B, C, D, E, F, G and H. The distance
between certain cities is indicated on the chart. (For example: A is 28
km from D.)
Find the distances between the neighboring cities.
Please, send your solutions to:
Solutions of previous problems