ABACUS International Math Challenge
for
3rd and 4th graders
December, 2003
A.401. The pirates store their jewelry
in boxes. (The masses of the boxes are indicated on the diagram.) Two boxes
contain gold, three boxes contain silver. One of the boxes contain pearl.
The sum of all the silver is twice as much as the sum of all the gold. How
many kilograms of pearl did the pirates collect?
A.402. There are six keys to the six boxes
in the captain's cabin. The keys are not marked in any ways. In the worst
case scenario, how many times does the captain have to put the keys in the
locks in order to open every box?
A.403. A merchant had a 40-kg weight. Once
he dropped it, and it broke into 4 pieces. When he measured the pieces,
it turned out that every one of them has a whole-number-kg mass, and with
the 4 pieces you can measure every whole-number-kg mass from 1 kg to 40
kg. What are the masses of the four pieces?
A.404. The pirates just robbed a ship.
The captain kept one quarter of all the gold from this latest catch, and
distributed the rest of it among his men: one half of the rest was divided
equally among his three officers, and then each of the 48 crew members received
25 pieces of gold. How many pieces of gold did they rob this time?
A.405. The pirates want to get to the cave
on Treasure Island, where they hide their treasures, as soon as possible.
Some pirates want to get on the island at White Bay, which is closer to
them right now, but others are suggesting to get off their ship at Blue
Bay, which is one more hour of sailing from White Bay. After some thinking,
the captain says to his men that no matter which bay they chose to get off
the ship, they will get to the cave in just the same time. How long does
it take to walk from each bay to the cave if it take 5 hours to walk from
one bay to the other going by the cave?
A.406. A few pirates row their boat to
an island to hunt for food for their ship. 8 of them shot rabbits, 7 of
them shot pheasants, 6 of them shot goats. 5 pirates shot both rabbits and
pheasants, 4 of them shot pheasants and goats, and 3 of them shot rabbits
and goats. Two pirates shot all three kinds of animals. How many pirates
were on the boat if only one of them did not shoot any animal?
A.407. Black Beard, the captain, has a
few golden cubes in his cabin. He stacked them in such a way that if he
looks at the pile from the front he sees this:
If he looks at the pile from the side he sees this:
What is the least and the most golden cubes that can be in the pile?
A.408. The pirates found eight bowls full
of golden coins. Later the captain discovered that one of bowls contains
copper coins instead, but the size and the shape of these coins are the
same as those of the golden coins.. He told his officers: "Every golden
coin has a mass of 2 dkg, but the mass of each copper coin is only 1.5 dkg.
The person, who uses the least number of measurements with a 2-arm balance
to find the fake coins, will get a prize. At least how many measurements
are needed?
Please, send your solutions to: