ABACUS International Math Competition
for
5th and 6th graders
March, 1998
B.49. Using every digit from 1 to 9 only once,
make up three 3-digit numbers, so that their product should be as low as
possible.
B.50. Find the greatest whole number in
which every digit (except for the first and last digits) is smaller than
the half of the sum of the two neighboring digits.
B.51. A servant's salary for a year was
$100 plus a set of clothes. However, the servant left his job after 7 months.
He received the set of clothes plus $20. How much is the set of clothes
worth?
B.52. Write numbers in the fields of a
5x5 grid, so that the sum of the numbers in any 2x2 part of the grid is
negative, while the sum of the numbers in the grid is positive.
B.53. In this addition same letters mean
same digits, different letters mean different digits. What number is 
?
B.54. The heads of a dragon are numbered
from left to right. "You may escape only if you cut off the heads of
this 7-headed dragon in a particular order." -was John warned by his
smart horse.
-"In the order, none of the heads may be cut off accordingly to
their numbers."
-"The first and the fourth head you cur off must be odd numbers."
-"After cutting off head number 6, you will have to cut off the
neighbors of this head only."
John escaped. In what order did he cut off the heads of the dragon?
B.55. We put a deck of 32 cards on the
table. Counting from the top of the deck every time, we take out every third
card. Then, from the remaining deck, we take out every fourth card. Now,
from the bottom up, the 8th card is the Ace of Hearts. Where was this card
in the deck we started with?
B.56. Using the following rules, we can
make several different number sequences: -start with 1;
-if b is an element of the sequence then the next element is 2b+1, or
if b-1 is divisible by 3 then the next element may be 
, also.
For example: 1, 3, 7, 2, 5, 11, 23, 47, ...
Following these rules, make a sequence that contains the number 8.
Please, send your solutions to:
Solutions of previous problems