ABACUS International Math Challenge
for
3rd and 4th graders
April, 1999
A.121. A number is called a Beprisque if
it is the only number between a prime number and a square of a number. One
such Beprisque is 10, since it is between 9 and 11. How many 2-digit Beprisques,
including 10, are there?
Jeffrey Mo, Grade 4, Canada
A.122. During a summer vacation it rained
7 times, but only either in the morning or in the afternoon. If it rained
in the morning then it did not rain in the afternoon. It did not rain on
5 mornings and on 6 afternoons. How many days was this vacation?
A.123. Find four positive whole numbers
so that if I add two of them I get the following results: 4, 5, 7, 8, 10,
11.
A.124. The sum of 13 different positive
whole numbers is 92. What are these numbers?
A.125. You have several 5x11 rectangles.
Using only these rectangles, can you make
a) a 39x54 rectangle?
b) a 39x55 rectangle?
(You have to use the small rectangles so that they cannot overlap each
other, but you may not have space between them, either.)
A.126. Write the numbers 1, 2, 3, 10, 11,
12, 19, 20, and 21 into the fields of a 3x3 grid so that the sum of the
numbers in each row, column and diagonal is the same.
A.127. There are a few red and a few green
balls in a box. Blind-folded, you have to take out 7 balls to have a red
for sure, and you have to take out 13 to have a ball from both colors for
sure. How many red and how many green balls are there in the box?
A.128. We placed planes against the sides
of a cube. How many sections is the space divided into by these 6 planes?
Please, send your solutions to: