ABACUS International Math Competition
for
5th and 6th graders
December, 1997
B.25. In each of the following expressions"equalities",
made out of little sticks, place one stick somewhere else so you would get
a true equality:
a) V=II+VIII
b) VII+V=III
c) VI=II+VIII
d) XI+XXX=X
B.26. We put a few equally sized cubes
on the table. If you look at them from the front and from the side, you
can see the following pictures:
At least how many cubes do you have to have on the table?
How many cubes can you have on the table at the most?
B.27. What is the smallest natural (non-negative
whole) number that is divisible by 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10?
B.28. How would you continue the following
sequence? Why?
1, 2, 4, 5, 7, 9, 10, 12, 14, 16, 17, 19, 21, 23, 25, 26,
...
B.29. 128, 69, 117, 51, 26, 40, 16, 37,
...
In this sequence the next element can be created by adding the squares
of the digits of the last number. (For example: the number following 16
is:
What is the 100th element of this sequence?
B.30. There are two 1's, two 2's and two
3's, and there is one digit between the 1's, two digits between the 2's,
and three digits between the 3's in the following 6-digit number: 231213.
Find a similar 8-digit number with two 1's, two 2's, two 3's, and two 4's.
B.31. Could the number 19971997 be the
product of two consecutive whole numbers?
B.32. Could the number 19981998 be the
sum of two consecutive whole numbers?
Please, send your solutions to:
Solutions of previous
problems