ABACUS International Math Challenge
for
3rd and 4th graders
December, 2002
A.345. On their trip around the world Fred
and Ben saw a beautiful paper dragon in China. The body of the dragon with
its head is 740 cm long. Its body is 460 cm longer than its head. How long
is the head of the dragon?
A.346. On their ship in the middle of the
Pacific Ocean, the boys are solving puzzles. Write the odd numbers 1, 3,
5, ..., 17 into the fields of a 3x3 grid so that the sums of the numbers
in each row, column and diagonal is 27.
A.347. On the ship there are 8 cabins for
storing luggage. All of them has a different lock on it. The captain gave
all 8 keys to Fred. The keys have no marks on them. In the worst case scenario,
how many tries does Fred need in order to find the right key to every lock?
A.348. During the trip the socks of the
boys got mixed up. In a bag there are 5 pairs of green socks and 5 pairs
of blue socks. You cannot tell the difference between a left sock and a
right sock. With their eyes closed, how many socks do they have to take
out of the bag so that they would have for sure:
a) 1 pair of socks?
b) 2 pairs of blue socks?
c) 1 pair of blue and 1 pair of green socks?
A.349. In the United States of America
the two boys bought a few bags of candies as presents. A few days later
they changed their minds and decided to eat them all. They opened all the
bags and started eating the candies randomly. However, 2 hours later they
could not eat any more. Then they counted the number of candies in each
bag and found that there was no empty bag, 3 bags had 1 candy in each, 3
bags had 2 candies in each, 3 bags had 3 candies in each, 3 bags had 4 candies
in each, and 2 bags had 5 candies in each. They decided not to keep all
the bags, but they fill up as many as they can, and then they throw away
the empty bags. How many empty bags can they throw away if 10 candies can
fit in every bag?
A.350. One rainy day the boys were on the
ship all day long. They kept on looking their analog watches (the ones that
have a long hand and a short hand), and came up with a problem to challenge
themselves: draw two straight lines across your watch to divide it into
three sections so that the sum of the numbers in each section is the same.
Could you help the boys?
A.351. One of the cabins on the ship has
a number combination lock that can be opened by a 4-digit number in which
the sum of the digits is 20. When you add 2 to the first digit, subtract
2 from the second digit, multiply the third digit by 2 and divide the fourth
digit by 2, the sum of these numbers is still 20. How many such 4-digit
numbers are there that can be used to open this cabin?
A.352. The last stretch of their trip the
boys completed by airplane. There were men, women and children on board.
Out of the 98 passengers there were 36 women, 47 men. 10 passengers were
English. How many English children could there be on board at most if there
is at least one English woman and at least one English man on board?
Please, send your solutions to: