ABACUS International Math Competition
for
5th and 6th graders
November, 1997
B.17. What is the sum of all those 3-digit
numbers with only odd digits?
B.18. You wrote down 1997 digits, one after
another, so that any two neighboring numbers would form a 2-digit number
that is divisible by 17 or 23. The last digit is 7. What is the first one?
B.19. Find a number that is twice the product
of its digits.
B.20. How many 0's are there at the end
of 1997!=1·2·3·...·1996·1997 ?
How long do we have to wait until we reach the year when this kind of
a product has more 0's at the end? What will the number of 0's be then?
B.21. There are two teams with 5-5 runners
in a running competition. The runner who finishes on the n-th place gets
n points. The team with the least total points wins. If every runner finished
on a different place, how many different total number of points could the
winner team have?
B.22. Draw 10 points, and connect some
of them with segments of straight lines in such a way that there would be
3 segments starting from each point and the segments would not intercept
each other.
B.23. How many 5-digit numbers are there
in which the sum of the digits is the same as the product of the digits.
B.24. Write whole numbers in a 5x5 grid,
so that in both diagonal directions, in every diagonal line (which could
contain 1, 2, 3, 4 or 5 fields) the sum of the numbers would be the same
(not 0) number.
Please, send your solutions to:
Solutions of previous problems