ABACUS International Math Challenge
for
5th and 6th graders
October, 2008
B.649. You write addition or subtraction
signs between the numbers in the sequence 1; 2; 3; 4; 5; ... so that you
would get 2008 as a result as soon as possible. What is the lowest possible
number in the sequence we have to go up to?
B.650. There are 11 girls and 16 boys in
a class. Their math teacher gives them 20 problems. Each problem is given
to either a boy, or a girl, or a boy-girl couple. Each problem is given
out only once, and each student has to work on only one problem. How many
boys and how many girls receive a problem on their own?
B.651. How many 2-digit positive whole
numbers are equal to the square of the sum of their digits?
B.652. We would like to cut up a rectangular
pan of cake into rectangular pieces. First we make a few cuts parallel to
two opposite sides of the pan, then we make a few cuts perpendicular to
these. We made a total of 13 cuts. Could the number of pieces be:
a) 45
b) 50?
B.653. Using five identical digits, parentheses,
and a few mathematical operations, create the number 30 in as many different
ways as possible.
B.654. In the following numbers: 1 - a,
2 - a, 3 - a, ..., 2008 - a what should we substitute for "a"
if the sum of these numbers is 7028?
B.655. Some square numbers remain squares
even if you write an extra digit 1 at the end of the number. Find the smallest
such positive square number.
B.656. Write down the positive 2-digit
numbers in an increasing order by using blue, red, and green pen in this
order continually for the digits. What is the color of the last digit 7
you have to write down?