ABACUS International Math Competition
for
5th and 6th graders
October, 1997
B.9. How can you divide 7 identical whole breads
fairly between 12 hungry men so that you would not cut any of the breads
into 12 pieces?
B.10. Find the greatest such 4-digit number
in which the sum and the product of the digits are the same.
B.11. Let's call a number lucky
if you can put its digits into two groups so that the sum of the digits
in both groups are the same. (For example: 34175 is lucky because
3+7=1+4+5.) What is the smallest lucky number with a lucky
neighbor?
B.12. Using every digit only once, write
down 3 numbers with a ratio of 1:3:5.
B.13. Five players agreed that after every
game the loser doubles everybody's money. They played 5 games and everybody
lost once. After the 5 games everybody had $128. How much money did each
of the players have before the games?
B.14. Draw 6 points and connect some of
them with segments of a straight line in such a way that out of every point
4 segments should start, and the connecting segments should not intersect
each other.
B.15. How many such 4-digit numbers are
there in which the sum of the digits is 5?
B.16. Write numbers (not all of them zero)
in the squares on a 5x5 grid so that the number in every square would be
the sum of the numbers in those squares that share a side with it.
Please, send your solutions by the end of October to:
Solutions of previous problems