ABACUS International Math Challenge
for
3rd and 4th graders
January, 2007
A.569. There are seven cards in a box with
a different number written on each card. Here are those numbers: 5; 84;
90; 613; 8; 75; and 605. At least how many cards do you have to pull out
of the box without looking so that among the cards pulled for sure there
is a(n):
a) even
b) 2-digit number
c) odd
d) 3-digit number
e)1-digit number
f) a number divisible by 5?
A.570. Henry has forty 5 cm x 10 cm cards.
Using some of them, how many different squares can he make if he may not
fold or cut cards, and he may not put one card on top of another? What is
the perimeter of the largest square?
A.571. Tamara has eight cards in front
of her in this order: 5; 1; 3; 7; 9; 0; 5; 2. (Each number is on a separate
card!) Which four cards should she take away so that the remaining four
cards when pushed together without changing their order would give:
a) the smallest possible 4-digit number
b) the greatest possible 4-digit number
c) the smallest possible 4-digit odd number?
A.572. Chris, Petra and Sam are running
races. They all have an equal number of candies to start with, but after
each race the last person gives two pieces of candy to the winner and one
piece of candy to the second place runner. There was never a tie for first
or second place. After 5 races Chris has 18 candies, Petra has 8 candies
and Sam has 4 candies. How many first, second and third places did each
of the kids have?
A.573. Frenchy was playing with the digits
2, 0, 0, 7. By mixing them up she created no-more-than-4-digit numbers,
and wrote them down in an increasing order. How many numbers did she write
down?
A.574. Danny has eight cards in front of
him with the following numbers on them: 6, 5, 9, 0, 3, 9, 4, and 1. Using
all these cards, how can he put together:
a) three numbers (two 3-digit numbers and one 2-digit number) with the:
i) greatest sum
ii) smallest sum?
b) two 4-digit numbers with the:
i) greatest difference
ii) smallest difference?
A.575. Tom has ten 6 cm x 12 cm cards.
Using some of them, how many different rectangles can he make if he may
not fold or cut cards, and he may not put one card on top of another? Which
rectangle has the largest perimeter?
A.576. Ronnie put the following numbers
(each on a separate card) in a hat: 0, 1, 2, 3, 4, and 5. She pulled out
two of them without looking, and added the two numbers. Which has a greater
chance (probability): that the sum is odd or even?
Please, send your solutions to: