ABACUS International Math Challenge
for
5th and 6th graders
September, 2000
B.193. Find five different integers that
have a product of 12.
B.194. The product of three consecutive
even numbers is the form of 87XXXXX8. (X does not necessarily means the
same digits.) Find the missing five digits.
B.195. Write the numbers 1, 2, 3, ...,
10 on the vertices and the midpoints of the sides of a regular pentagon
so that the sums of the three numbers on every side is the same.
B.196. The director of a zoo placed 9 llamas
in a square-based cage as shown on the diagram. Strangely enough these llamas
are very lazy, so they stay in their given locations for a long time. Could
you provide each llama with its own cage just by building two more square-shaped
fences?
B.197. On a disk I wrote the number 1,
on two disks I wrote the number 2, on three disks I wrote the number 3,
..., on fifty disks I wrote the number 50. I put all of the 1+2+3+...+50=1275
disks in a box. How many disks do you have to take out without looking so
that for sure you have at least 10 disks with the same number on them?
B.198. Father and son are in a race. The
father can make 6 steps while his son makes 7. The son already made 30 steps
when his father left the starting point. The father needs 3 steps to cover
the same distance as the son makes with 5 steps. How many steps does the
father need to catch up with his son?
B.199. Starting at age 4, each of two sisters
receive as many books on their birthdays as many years old they are that
day. How old are the girls when the total number of books they ever received
is 100?
B.200. A girl and a boy are talking to
each other:
"I am a boy." -says the one with black hair.
"I am a girl." -says the one with red hair.
What color is the boy's hair if at least one of them is not telling
the truth?
Please, send your solutions to: