ABACUS International Math Challenge
for
5th and 6th graders
January, 2006
B.521. My family and my mom's friend, Maria,
live on the same bike path. My mom said that if I bike from our house to
Maria's house and back to our house, I will get an ice cream. Usually my
speed is 10 miles per hour. The distance between my house and Maria's house
is 1 mile. My mom can walk to Maria's house in 20 minutes and Maria can
walk to our house in a half an hour. They decided to meet on the bike path,
so they left at the same time. Because I wanted my ice cream sooner I left
with my mom and biked from my mom until I reached Maria and went back to
my mom. When I met my mom I went back to Maria and so on until they met
each other. Did I bike enough to get my ice cream by the time they met each
other?
by Bilyana Tzolova, Pennsylvania
B.522. You divide a positive whole number
by 1995, and you get a remainder of 75. What is the remainder if you divide
the original number by 57?
B.523. What is the smallest prime number
that can be written as the sum of 5 different prime numbers?
B.524. A 3-digit number increases by 9
when you switch its digits in the ones and the tens place. It increases
by 90 if you switch its original digits in the hundreds and the tens place.
How much will it increase if you switch its original digits in the ones
and the hundreds place?
B.525. What number is under 144 if you
continue writing the numbers in the following number pyramid?
B.526. There are boys and girls in a group.
After 15 girls left, the number of boys is twice the number of girls present.
Now 45 boys went home, and in the remaining group there are 5 times as many
girls as boys. How many girls were there originally in the group?
B.527. Can you arrange the digits 1,1,2,2,3,3,4,4
into an eight-digit number where the 1s are separated by exactly one digit,
the 2s by two digits, the 3s by three digits and the 4s by four digits?
by Kuangran He, Iowa
B.528. Four people (A, B, C, and D) are
playing cards, and after every game they write down who owes how much to
whom. After a few games you can read the following notes on the paper: A
owes B $5 and C $4, B owes D $3, C owes B $7, D owes C $8 and A $6.
a) Who won and who lost the most money so far?
b) How could all the payments be made be moving the least amount of
money?