ABACUS International Math Challenge
for
5th and 6th graders
December, 2003
B.401. I went apple picking last weekend.
15 of the first 20 apples I picked were healthy (no bugs in them). 1/3 of
the apples I picked after that was healthy. This way half of all the apples
I picked were healthy. How many apples did I pick?
B.402. A flea is jumping on a number line.
Every time it jumps from one whole number to a neighboring whole number,
either left or right. It starts from Zero. How many different ways can it
get to 6, or to negative 3 in 8 jumps?
B.403. We color the sides of a cube by
blue and green, so that each side is only one of these two colors. How many
different cubes can we make? (Two cubes are considered to be the same if
you can rotate one of them into the position of the other cube.)
B.404. There are 3 kinds of pastries in
a bakery: bagels for 35 cents each, slices of cheese cake for 50 cents each,
and muffins for 65 cents each. Every time Victoria goes shopping, from her
coins and bills she gives just as much money as necessary to pay for the
items she buys. (The available coins are 1 cent, 5 cents, 10 cents, 25 cents
50 cents, and the available bills are $1, $5, $10, $20, $100, but she does
not necessarily have all of them.) This time she puts a total of 100 cents
on the counter and says: "May I have one, please?" The salesman
looks at the coins and knows without a question what to give her. (The salesman
did not see what kinds of coins in Victoria's purse were.) What did she
buy?
B.405. Using the digits 1, 3, 4, 5, and
one more digit of your choice, write down the greatest 5-digit number that
is divisible by 12.
B.406. On the market a man is selling eggs.
Some of his baskets have chicken eggs, the others have duck eggs. The numbers
of eggs in the 6 baskets are: 4, 6, 12, 13, 22, and 29. The man points to
one of his baskets and says: "If I sell this basket of chicken eggs
then I will have twice as many chicken eggs as duck eggs." Which basket
is he talking about? How many baskets have duck eggs in them?
B.407. Timea's age is a 2-digit number.
If you multiply this number by the product of its digits, you get a 3-digit
number with identical digits. How old is Timea?
B.408. We glued together 7 regular dice,
which are not necessarily marked with the dots the same exact way, to get
the U-shaped figure on the diagram. We glued the figure onto a cardboard.
We cannot see the dots on the sides shaded on the diagram. At least how
many dots are there all together on the glued sides?
Please, send your solutions to: