ABACUS International Math Competition
for
7th and 8th graders
December, 1997
C.25. After thinking for a long time, Julie
divided the first figure into 4 parts of the same size and same shape. Now
you have to divide the first figure into 5 parts of the same size and same
shape. How can it be done?
C.26. Is the following sum even or odd?
Why?
C.27. Find all those 4-digit numbers that
are equal to the 4th power of the sum of their digits.
C.28. Prove that the following sum is divisible
by 100:
C.29. Find the smallest positive multiple
of 36 with even digits only.
C.30. With the appropriate order of the
digits 1, 2, 3, 4, 5, 6, 7, 8, and 9, find the smallest 9-digit number that
is divisible by 99.
C.31. Find the smallest positive whole
number that ends with 56, divisible by 56, and the sum of its digits is
56.
C.32. Find all those 4-digit
numbers that
are divisible by 4, where 
is divisible by 7, 
is divisible
by 5, and 
is divisible by 9.
Please, send your solutions to:
Solutions of previous
problems