ABACUS International Math Challenge
for
7th and 8th graders
September, 1999
C.129. We wrote a number on each side of a
cube. The sums of the numbers on the opposite sides of the cube are the
same. The three numbers you cannot see on the diagram are prime numbers.
What are these numbers?
C.130. What are the last two digits of
the number N=1!+2!+3!+4!+...+1998!+1999!
Péter Kocsis, Hungary
C.131. Find such a 5-digit number that
reverses the order of its digits when multiplied by 4.
C.132. Let's call the numbers that are
the products of two primes "barely composites". How many barely
composite positive numbers are there below 2000?
C.133. Let ABCD be such a parallelogram
where side AB is twice as long as side AD, and the angle between them is
60 degrees. Let BEFC be a rhombus where point E is on the extension of side
AB, closer to point B. Which segment is longer: BD or BF?
Péter Kocsis, Hungary
C.134. Find a 3-digit number in base 10
that is 5 times as much as the product of its digits.
C.135. On a 5x5 chess board, we want to
send a piece from the top left to the bottom right corner. The piece can
move only one field at a time either to the right or down. We want to pick
a field where the piece is not allowed to step onto. Which field should
this be if we want the piece to have the least number of options to make
this trip, but we want it to get there?
C.136. A flee is jumping on a coordinate
system from one point that has whole-number coordinates to one of the neighboring
such points. The flee always jumps either horizontally or vertically. How
many different location s can the flee be after 100 jumps, if it started
from the origin?
Please, send your solutions to: