ABACUS International Math Challenge
for
5th and 6th graders
February, 2003
B.361. Three men are sitting in a row;
the Truthful, who is always telling the truth; the Liar, who always lies;
and the Joker, who either lies or tells the truth but you never know with
him. We asked the one sitting on the left: "Who is sitting next to
you?" He answered: "The Truthful". We asked the one sitting
in the middle: "Who are you?" He answered: "The Joker."
We asked the one sitting on the right: "Who is sitting in the middle?"
He answered: "The Liar." Who is sitting where?
B.362. See if you can determine the final
product. Your only other hint is that the problem does NOT contain any sevens.
Joe Connelly, Savage, MN USA
B.363. Ben participates in a multiple choice
Math Competition, where you have to pick the correct answer out of 5 answers
given. You get 4 points for a correct answer, you lose one point for an
incorrect answer, and you get zero point for a question you do not answer.
Ben did not know the answer to some of the questions, so he just guessed
the answer for those questions. Two of his guesses happened to be correct.
It turned out also that he would have gotten 2 more points if he left blank
all those questions he guessed on. How many answers did Ben guess?
B.364. Continue this number sequence: 10,
11, 12, 14, 18, 26, 32, 35, ....
Michael Do, Sydney, Australia
B.365. Mr. and Mrs. Smith and their neighbors,
Mr. and Mrs. Taylor, were giving cherries to their own grandchildren. Every
grandson received as many cherries as many grandsons each couple has, and
every granddaughter received as many cherries as many granddaughters each
couple has. Both couple gave away 697 cherries, but the two couples have
a different number of grandchildren. How many grandchildren do the two couples
have together?
B.366. Romeo was looking for three such
prime numbers that would add up to 432 and their product would be 1234567.
But when all of his work was fruitless, he called Julia for help, who thought
about it a little and said that there are no such primes. How did she know?
B.367. 8 children can eat 12 sheets of
chocolates in 3 days. How many sheets of chocolates can 9 children eat in
4 days, if everybody eats the same amount every day?
B.368. The average height of 15 children
is 130 cm. However, it turned out that the nurse did not measure Pete's
height, instead she measured John's height twice. If she did, the average
height would have been 136 cm. How much taller is Pete than John?
Please, send your solutions to: