ABACUS International Math Challenge
for
7th and 8th graders
September, 1998
C.65. How many different ways can you write
1998 as the product of two whole numbers?
by Bognár Ferencné, Hungary
C.66. On a table tennis tournament everybody
plays everybody. The organizers of the tournament wanted to reduce the number
of games by 50, therefore they invited 4 less players then originally planned.
How many competitors did participate on this tournament?
C.67. What is the last digit of:
by Bognár Ferencné, Hungary
C.68. Find the smallest prime number that
is the sum of two primes, and it is the sum of three different primes, and
it is the sum of four different primes, and even more, it is the sum of
five different primes, too.
C.69. The first element of a number sequence
is 2, the second element is 3. The next element, from here on, can be calculated
by subtracting the one before last element from the last element. (Therefore,
the third element is 3-2=1.) What is the sum of the first 1998 elements
of this sequence?
C.70. A bicyclist and a pedestrian leave
point A at the same time traveling with a constant speed to get to point
B. The bicyclist when reaching point B turns right back and meets the pedestrian
1 hour after they left point A. Now the bicyclist turns right back again
and they both go towards point B. When the bicyclist reaches point B, he
turns right back again and meets the pedestrian 40 minutes after their first
meeting. How long does it take the pedestrian to get from A to B?
C.71. Using six 2's and two 1's, find an
8-digit number that is divisible by 7.
C.72. Fill in a 6x6 grid with the numbers
-1, 0, and 1, so that there would not be two equal sums when you add the
numbers in each row and column. (With other words, every field in the grid
has to be filled with one of the following numbers: -1, 0, 1, so that when
you calculate the sum of every row and every column, every result should
be different.)
Please, send your solutions to: