B.129. Put the letters of the word ABACUS in
every possible order. Then write these 6-letter "words" one after
the other in alphabetical order. Which is the 100th word?
Péter Kocsis, Hungary
B.130. Find such a 4-digit number that
reverses the order of its digits when multiplied by 4.
B.131. How many different ways can you
get from A to B if you cannot step on the fields with an X, and you may
make a step one field to the right or one field down.
A
X
X
X
X
B
B.132. Which numbers are there more of:
the abaaba type 6-digit numbers that are divisible by 3, or the abaaba type
6-digit numbers that are divisible by 7?
B.133. Fill in the blanks in the following
box with numbers written in base 8, so that the statement in the box is
true:
In this box there are exactly ..... digit 0's, ..... digit 1's, ....
digit 2's, .... digit 3's, .... digit 4's, .... digit 5's, .... digit 6's,
and .... digit 7's.
B.134. There are 25 students in a class
out of which 17 know how to ride a bicycle,13 knows how to swim, and 8 knows
how to ski. None of them does all three of these sports, but every bicyclist,
every swimmer and every skier is good or medium in math. 6 students in this
class are weaker than medium in math. (The possible grades in this school
are: excellent, good, medium, poor, and inadequate.)
How many students in this class are excellent in math? How many swimmers
can ski?
Péter Kocsis, Hungary
B.135. Find the smallest 12 consecutive
6-digit numbers out of which the greatest is divisible by 12, the second
greatest is divisible by 11, the one that is one smaller than that is divisible
by 10, and so on ... and finally, the second smallest is divisible by 2.
B.136. Break up the number 11111211111
into the product of two whole numbers (both greater than 1).