ABACUS International Math Challenge
for
5th and 6th graders
November, 2003
B.393. Sara has 3 red, 3 blue and 3 green
pearls. She would like to arrange them on a 3x3 grid so that every row and
every column has one of each color. She considers two arrangements to be
different if she can see at least one difference from her point if view.
How many different arrangements can she possible make then?
B.394. You are looking for mines on the
following grid. If you click on a field that has a mine on it, the mine
blows up, but if there is no mine on the field then a number will pop up
in that field indicating how many of the neighboring 8 fields have a mine
on them. You know that there are 4 more mines on the grid. Where are they?
B.395. This school year started on Monday,
September 8th. What day of the week is the 2003rd day after this?
B.396. Find the greatest 2-digit number
which is divisible by the sum of its digits.
B.397. We painted red all sides of a cube
with a whole number length unit long edges. Then we cut it up to unit cubes.
It turned out that there are 48 less of those unit cubes with no paint on
them than those with paint on them. How many times more unit cubes have
paint on them than those with no paint on them if there are less than 1000
unit cubes?
B.398. On an 8x8 chess board there is a
white figure in one corner and a black figure in the diagonally opposite
corner. Each figure at each turn may move one step to the left, right, up
or down. They may not move diagonally. One figure can hit the other figure,
and win the game, if it can move onto the field where the other figure is.
White makes the first move, and then they alternate. Prove that white can
never win this game.
B.399. Tori starts writing the squares
of the consecutive positive whole numbers starting with 1. What is the 2003rd
digit Tori has to write down?
B.400. Timmy's favorite picture in her
book is on the sheet which has 7 more sheets in front of it than behind
it in the book. The book has 136 pages. What page could the picture be on?
(The covers are not numbered pages, therefore, they are not considered sheets
of the book, either.)
Please, send your solutions to: