ABACUS International Math Challenge
for
3rd and 4th graders
January, 2000
A.161. Can you divide the numbers 1, 2,
3, ..., 1998, 1999 into two groups so that the sum of the numbers in each
group is the same.
A.162. There are 600 students in a school,
30 students in every class. Every student has 5, and every teacher has 4
lessons every day. In every lesson there is a full class and one teacher
together. How many teachers are there in the school?
A.163. Two people are playing cards. They
bet $10 each on every game. In the end when they were done playing, one
of the players won 3 games but lost a total of $70. How many games did they
play?
A.164. Grandma, expecting her grandchildren
to visit, baked some cookies. She counted the cookies and said to herself:
"If I want to give 5 cookies to every one of them, I need to bake 3
more cookies, but if I give them 4 each, I have 3 cookies left over."
How many grandchildren does grandma have?
A.165. In the Smith family there is a tradition
that at the end of each school year the father gives the same number of
books to each of his 3 children as the number of the grade they each completed
that year. One year the children reached a total of 25 books. What grades
did they complete that year?
A.166. A traveler arrives to a motel. On
his way there he was robbed so thoroughly that all he has left is a necklace
that is made of 7 golden coins connected to each other by little rings.
The owner of the motel offered bed and food for a coin every day. The traveler
paid his bill every evening. How could they do this without having have
to cut off every coin from the necklace, even if the traveler stayed for
7 days?
A.167. All the seven dwarves, coming home
from the mine, bring a present for Snow White. Each dwarf brings her a golden
chain made of seven golden rings. Sneeze lost one of the rings on the way
home so he gave Snow White a chain with only 6 rings. What is the least
number of rings Snow White has to open in order to make one big closed necklace
from these chains?
A.168. The seven dwarves made a schedule
for the 31 days of a month, so they would know who supposed to sweep their
little house each day. Sneezy sweeps on Mondays, Sleepy sweeps on Tuesdays,
Doc sweeps on Wednesdays, Happy sweeps on Thursdays, Grumpy sweeps on Fridays,
Bashful sweeps on Saturdays and Dopey sweeps on Sundays. Sneezy and Grumpy
said that they swept exactly 4 times that month. Who swept on the first
day of the month?
Please, send your solutions to: