ABACUS International Math Challenge
for
3rd and 4th graders
September, 1998
A.65. One after the other you write down
the numbers from 1 to 1998 . Which digit is on the 1998th place?
by Bognár Ferencné, Hungary
A.66. What number can you write in place
of the question mark, and why?
A.67. How many different ways can you get
1998 as the sum of identical numbers?
by Bognár Ferencné, Hungary
A.68. Two strange men live in Strange country:
Peter, who lies every Monday, Tuesday and Wednesday, but tells the truth
on all the other days; and Paul, who lies on every Thursday, Friday and
Saturday, but tells the truth on all the other days. One day they said:
Peter: "Yesterday I had one of my lying days."
Paul: "Me, too."
What day of the week was that?
A.69. During a summer vacation it rained
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.70. Once upon a time a fictitious fox
made the following arrangement with a young man: Every time the man crosses
the bridge, the fox doubles his money and then the man has to pay $24 customs
to the fox. The young man thought that he could make a lot of money this
way, but soon he was very disappointed. After he crossed the bridge for
the third time and he paid the customs, he had no money left. How much money
did he have when he met the fox?
A.71. You paint a 10x10x10 cube black,then
with cuts parallel to the sides you cut the cube into 1x1x1 cubes. How many
little cubes have:
a) at least one black sides;
b) exactly one black side?
A.72. There are five balls in a row: a
yellow, a brown, a blue, a red and a green. Find their order if you know
that the blue ball is not in the middle; the red is the same distance from
the blue,as the blue is from the green; the left-side neighbor of the yellow
is the red ball.
Please, send your solutions to: