ABACUS International Math Challenge
for
5th and 6th graders
September, 2005
Please, note the new address you
have to send your solutions to at the bottom of this page!!!
B.489. In a room there is a digital clock
which shows the time using four digits in the form of hours:minutes from
00:00 to 23:59. At what times does the clock give out the least and the
most light if the digits are the following:
B.490. We arranged the consecutive positive
whole numbers in the chart below. (The first number in each row indicates
how many numbers we wrote in that row.) Where on this chart is the number
490?
B.491. Using all of them, write the numbers
0, 1, 2, 3, 4, 5, 6, 7, 8 in the circles of the diagram below so that the
sum of the numbers in the three inner circles is a third of the sum of the
numbers in the six outer circles. What number triplets can be written in
the inner circles?
B.492. There are 1-, 2-, or 3-legged cherries
in a basket, 7 of each kind. Pete and Agnes are taking turns in picking
a cherry out of the basket. If they pick one fruit of a 2- or 3-legged cherry
then they take the 1 or 2 other cherries connected to the one they picked,
too.
a) What could the greatest difference in the total numbers of cherries
they took out of the basket be?
b) Could it happen that they both take out the same total number of
cherries?
B.493. To put a figure on each of the fields
on the edges and each field of one of the diagonals of a square-shaped chess-like
board we used 64 figures. How many empty fields are still there on this
board?
B.494. We wrote down all the 3-digit numbers
in an increasing order, so that we used a red pen for the even numbers'
digits and a blue pen for the odd numbers' digits. How many red zeros are
there on the paper?
B.495. In the following product (AxBxAxCxUxS)
x (IxLxOxVxExIxT) different letters mean different digits, the same letters
mean the same digits. What is the ratio of the greatest and the smallest
possible values of this product?
B.496. Tim built the 5-story tower (see
the diagram below) in the corner of his room. He used 35 identical little
cubes. How many stories would the tower have if he used 220 of his cubes
the same way?
