ABACUS International Math Challenge
for
5th and 6th graders
September, 2003
B.377. If you fold the following diagram along the lines, you can make a cube. At every vertex, calculate the product of the numbers on the sides running into that vertex. Which one of these products is the greatest?
B.378. The following figures are cut out from red cardboard paper. (Only the side facing up is red.) How many red rectangles can you put together by using all of these pieces?
B.379. We know the following about the distances between 4 points (A, B, C, D) in the same plane: AB = 15 cm, BC = 92 cm, CD = 36 cm, and AD = 41 cm. How far is point A from point C?
B.380. A, B, C, D, E, and F are different one-digit numbers. A, B, C, and D are consecutive numbers in this order, and A is the smallest of the four of them. The product of AB and CD is equal to EFBD, where AB and CD are 2-digit numbers, and EFBD is a 4-digit number. Find such digits for A, B, C, D, E, and F.
B.381. The product of four consecutive numbers is 3024. Find these numbers.
B.382. How many digits are there in the product of 
,
, and 
?
B.383. On a rectangular shaped table a fly is walking from one corner to the opposite corner along the diameter, but it stops at the third of the road. At that point the fly is 40 cm from one side of the table and 56 cm from another side of the table. What could the area of the top of the table be?
B.384. There are only turkeys and rabbits in a backyard. There are 84 more legs than twice the number of heads in the backyard. How many rabbits are there in the backyard?
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