ABACUS International Math Challenge
for
3rd and 4th graders
September, 2001
A.257. If you want
to get in Mr. Dagobert's treasure cellar
you have to turn one of these dominoes up-side-down, so that the sum of
the little circles is 21 in both the top and the bottom row. Which domino
do you have to spin around?
A.258. Three ducklings: Nicky, Ticky and
Vicky, are playing with dice. They are rolling 3 dice at a time. The following
statements are made about the sums of the numbers on the tops of the three
dice. Decide about each statement whether it is true for sure, maybe true
but not sure, or cannot be true.
a) It is greater than 18.
b) It is greater than 3.
c) It is less than 18.
d) It is even.
e) It is exactly 3.
f) It is at least 3.
A.259. Maestro Danny discovered the paint
that turns things into gold. He starts painting eggs, when Captain Quack
joins him. While Danny paints 4 eggs, Quack paints 3. In a half an hour
they already painted 63 eggs. How many golden eggs did they each make?
A.260. Move one of the sticks, so that
the equality is true:
A.261. The bank robber Beagle brothers
lie a lot. The youngest one lies every Monday, Wednesday and Friday, but
he tells the truth on the other days. The oldest one tells the truth every
Tuesday, Wednesday and Thursday, but lies on all the other days. One day,
when they met in front of the bank, the youngest one said proudly: "I
told the truth yesterday." "Me, too." replied the oldest
one. On what day of the week did they meet?
A.262. The other Beagle boys are in jail,
completing their 10 month sentences. No matter how angry the judge was at
them, he promised them that he would half their time if they found 10 consecutive
whole numbers with a sum that is divisible by 10. Are there such 10 numbers?
Reason your answer.
A.263. Mr. Dagobert goes shopping with
1000 single dollar bills. He wants to put the bills into 10 bags so that
he is able to pay any amount of whole dollars up to $1000 just by giving
away a few well-selected bags. How should he place his money into the bags?
A.264. There are gold and silver fish swimming
in Martha's fish tank. There are 5 times as many gold fish than silver fish.
One of the silver fish died but she replaced it with a gold fish, so now
there are 7 times as many gold fish than silver fish. How many gold and
how many silver fish where in the tank originally?
Please, send your solutions to: