ABACUS International Math Challenge
for
3rd and 4th graders
September, 2003
A.377. There are many necklaces among the Pharaoh's jewelry. 1/3 of the necklaces are made with emerald, and 1/4 of them (that is 24 necklaces) are made with zephyr. How many necklaces have emerald?
A.378. Write different positive whole numbers into the stones of the pyramid so that every number is the sum of the two numbers directly underneath it, and the top number is a s little as possible.
A.379. Camels with either one or two humps are traveling across the desert. All together they have 14 humps and 40 legs. There is a Bedouin riding on every other 2-hump camel. How many Bedouins are traveling with the camels?
A.380. Out of the numbers 1, 2, 3, ..., 99, 100, pick out as many as you can so that you would not have picked such two numbers whose sum is picked, also.
A.381. There is a number-code lock on the door of the Pharaoh's jewelry room. It opens with a particular 3-digit number. We know that the sum of the digits of the code is a 2-digit number that you can also get by covering the code's last digit. The code actually is the greatest one of these numbers. Which 3-digit number opens the lock?
A.382. A goldsmith has to decorate 12 jewelry boxes with gold. For this he has 7 identical gold plates. How can he divide the 7 plates equally into 12 pieces without cutting any of the plates into 12 or more equal pieces?
A.383. You have 1000 one-dollar coins. Separate them into 10 bags in such a way so that you could pay any amount of money up to $1000 by giving away a few of your bags.
A.384. In the gigantic Kheops Pyramid there are about 2 and a half million stone cubes put in 206 horizontal rows. They used cubes of sandstone, limestone and granite to build it. The mass of 2 granite cubes is the same as the mass of 5 limestone and 2 sandstone cubes together. 3 limestone cubes have the same mass as 6 sandstone cubes. How many sandstone cubes have the same mass as 5 granite cubes?
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