ABACUS International Math Competition
for
3rd and 4th graders
February, 1998
A.41. What figure fits in the place of
the question mark?
A.42. Write 
(addition, subtraction,
or multiplication) signs between the following numbers, so that the equality
would be true. ( Do not use parentheses.)
a) 7 3 2 5 8=10
b) 5 5 2 5 5=10
c) 8 2 4 6 4=10
d) 6 3 4 2 6=10
e) 4 3 5 3 5=10
A.43. In this addition same letters mean
same digits, different letters mean different digits. What numbers did we
add?
A.44. How many eggs are there in a basket
if you would have 2 eggs left over when taking the eggs out in groups of
3, you would have 3 eggs left over when taking the eggs out in groups of
4, and you would have 4 eggs left over when taking the eggs out in groups
of 5.
A.45. Let's write the numbers from 1 to
60 one after the other: N=123...5960. Delete 100 digits from this number
so that you would get the highest possible number when you push the remaining
digits close together. What is this number?
A.46. Smarty decided that from now on he
is going to tell the truth on Mondays, Wednesdays and Fridays, but will
lie on all the other days. Once he said: "Tomorrow I am going to tell
the truth." On what day did this happen?
A.47. Using the digits 1, 2, 3, 4, 5, 6,
(any digit may be repeated any number of times) I wrote down a 4-digit number.
A few people tried to guess my number. The first try was 4215. Two digits
are correct, but only one of them is in the right place. The second try
was 2365. Again, two digits are correct, but only one of them is in the
right place. The third try was 5525, but here they didn't even get the digits
right. Now, could you tell me what my number is, or you could take a wild
guess only?
A.48. We put 48 pebbles in 3 groups so
that the first group has 11 pebbles, the second group has 14 pebbles, and
the third group has 23 pebbles. In every step you may move so many pebbles
from one group to another that the number of pebbles in the target group
would double. Even out the number of pebbles in the groups in the least
number of steps.
Please, send your solutions to:
Solutions of last year's
problems