ABACUS International Math Challenge
for
7th and 8th graders
April, 2001
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on the bottom of this page!
C.249. Rabbit, Pooh and Piglet are playing
on different musical instruments. One of them plays the recorder, another
one plays the drums, and the third one plays the guitar. Based on the following
statements, find out who plays on what instrument.
Rabbit: "I visited Tigger with my friend who plays the recorder."
Pooh: "I went to pick berries with the drummer."
Piglet: "I gave a concert with Rabbit and the guitarist for Christopher
Robin."
C.250. Find the integers a and t
for which the following equation is true:
by Doni Rácz, Newport Beach, California
C.251. Find the smallest positive whole
number that is divisible by 28, the sum of its digits is 28, and ends with
28 in base 10.
C.252. There is an 11x6x5 solid made up
of unit cubes. A termite chewed through it by one of its diagonals. How
many unit cubes did the termite chew through?
C.253. The longer side of a rectangle is
twice as long as the shorter side. Cut it up to 8 triangles so that every
angle in these triangles is less than 90 degrees.
C.254. Pick nine different numbers out
of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and place them in a 3x3 grid,
so that the sum of any two numbers whose fields share a side is a prime
number.
C.255. How many digits are there in the
standard form of 
in base 10?
C.256. Mr. Smith lives in a house on Nowhere
street, and his house number is between 13 and 1300. Mr. Taylor is curious
to find out Mr. Smith's house number, so he starts asking Mr. Smith a few
questions.
Mr. Taylor: "Is your house number greater than 500?" Mr. Smith
answers the question, but he is lying. (However, Mr. Taylor does not know
this.)
Mr. Taylor: "Is it a square number?" Mr. Smith answers the
question, but he is lying again. (However, Mr. Taylor does not know this.)
Mr. Taylor: "Is it a cube number?" Mr. Smith answers the question,
and this time he is telling the truth.
Mr. Taylor: "Now, if you tell me whether the one before last digit
is 1 or not, then I can tell your house number." Mr. Smith responds.
Then Mr. Taylor tells him the house number he thinks is correct. However,
Mr. Smith says that Mr. Taylor is incorrect.
What is the house number of Mr. Smith?
Please, send your solutions to: