ABACUS International Math Challenge
for
3rd and 4th graders
September, 1999
A.129. The sum of the numbers in two neighboring
fields is in the field right above them. Fill in the blanks.
A.130. How many positive even numbers are
there in which the sum of the digits is 8 and the product of the digits
is 6?
A.131. Similarly to the following 4x4 grid
we fill in a 100x100 grid. What is the sum of the numbers in that grid?
| 1 |
2 |
3 |
4 |
2 |
3 |
4 |
5 |
3 |
4 |
5 |
6 |
4 |
5 |
6 |
7 |
A.132. Anna, Bea, Cecilia, Dori and Elizabeth
are collecting phone cards. Bea has twice as many cards as Anna, and a third
of what Cecilia has. Dori has four times as many as Cecilia and a fifth
of what Elizabeth has. They have 459 cards all together. How many cards
do they have each?
A.133. It happened in 1932 when I was exactly
the same number of years old as the number created from the last two digits
of the year of my birth is. When I mentioned this to my grandfather, he
said that the same thing is true for him. How old were we then?
A.134. Find such a 4-digit number that
reverses the order of its digits when multiplied by 9.
A.135. In the series 0, 1, 2, 3, 4, 5,
6, 7, 8, 9 the sums of the neighboring elements is 1, 3, 5, 7, 9, 11, 13,
15, 17. Here the numbers increase by two. Put the numbers 0, 1, 2, 3, 4,
5, 6, 7, 8, 9 in a series so that the sums of the neighboring elements increases
by one.
A.136. There are three groups of matches
on the table. In the first group there are 11, in the second group there
are 7, and in the third group there are 6 matches. In a step you may double
the number of matches in a group by using some of the matches of one of
the two other groups. Try to make the number of matches in each group the
same in the least number of such steps.
Please, send your solutions to: