ABACUS International Math Challenge
for
5th and 6th graders
December, 2002
B.345. Using all non-zero digits exactly
once, write down 3 numbers so that the one of them is three times, the other
is five times greater than the smallest number.
B.346. The perimeter of a triangle is 2002
cm. The longest side is 337 cm longer than the middle, which is 330 cm longer
than the shortest side. How does this triangle look like (how long are its
sides)?
B.347. A number is called "lucky"
if its digits can be put in two groups so that the sum of the digits in
each groups is the same. (For example: 32384 is "lucky" because
3+3+4=2+8) Find the smallest positive "lucky" number with a "lucky"
neighbor.
B.348. There are 13 couples on a party.
Every man shook hands with everybody except for his own wife, but the women
did not shake hands with each other. How many handshakes took place?
B.349. How many positive whole numbers
give the same remainder as the quotient when divided by 4?
B.350. Five numbers are written on a piece
of paper. You get the following sums when you add any two of them: 3, 5,
6, 9, 10, 10, 11, 12, 13, 17. Find these five numbers.
B.351. On a video tape you can make a 2-hour
program with slow recording speed, a 4-hour program with medium recording
speed, or a 6-hour program with fast recording speed. On your tape you have
already recorded 32 minutes of program with slow recording speed and 44
minutes of program with medium recording speed. How many more minutes of
program can you record on this tape with fast recording speed?
B.352. Peter is planning a 4500 km car
trip. His favorite tires wear off after 3000 km and you have to change them.
He has brand new tires at the beginning of the trip. At least how many more
new tires does he need to take with him for this trip, and how does he have
to change them in order to complete his trip?
Please, send your solutions to: