ABACUS International Math Challenge
for
3rd and 4th graders
October, 2002
A.329. There are a lot of geese on the
market for sale. The sum of their heads and legs is 99. How many geese are
there?
A.330. A cowboy has to count his cows.
To make the job more interesting he decides that, while counting, he will
say "bang" for every number that is divisible by 3 or in which
the difference of the digits is divisible by 3. How many times did he say
"bang" if he counted 38 cows?
A.331. The new major of a small village
hates the number 3. Therefore, he ordered every house-number sign with the
digit 3 on it to be removed. How many signs were removed from the three
streets of the village if the number of houses in each were 50, 80, and
100? (There are the same number of houses on each side of each street.)
A.332. A witch changed three policemen
(Steve, Jack, and Bill) into frogs. The captain of the local police department
asked all three frogs about who they were. They gave the following answers:
Red frog: "I am Steve."
Yellow frog: "The green frog is not Steve, and I am not him either."
Green frog: "I am not Bill."
Who is who if we know that one of them was lying?
A.333. On the market you can get a duck
for two chickens. A goose costs you two ducks and two chickens. How many
chickens do you have to give for a goose?
A.334. While a cowboy was counting his
46 cows, he came up with a game. Instead of the following numbers, he said
"bang": 4, 8, 12, 13, 16, 17, 20, 22, 24, 26, 28, 31, 32, 35,
36, 39, 40, 44. How did he pick these numbers? (How did he set the rules
of the game?)
A.335. A carpenter is building a 5-story
tower. (There are 5 floors above the ground floor.) Every floor is connected
to the next one by the same number of steps in the staircase. The carpenter
called down to his assistant to bring up a barrel of water from the ground
floor to the top of the tower, but he dropped the barrel on the second floor
and it rolled back down to the ground floor. The assistant had to go back
and get it. This time he was more careful and made it up to the top. He
took a total of 216 steps to complete this assignment. How many steps are
there between two consecutive floors?
A.336. The servants of the king are eagerly
looking for the magic herbs on the field to cure the king's illness. Shoulder
to shoulder they carefully comb the 50-meter-long field by taking two steps
forward and one step back. How many steps do they take forward and how many
back if every step is 50 cm long?
Please, send your solutions to: