ABACUS International Math Challenge
for
3rd and 4th graders
March, 2008
A.633. One Sunday afternoon a family went
on a tour boat ride around the island of Manhattan starting at 42nd Street.
Susan observed that although many people were already on the boat, at the
23rd Street station 4 German and 3 Danish men, and 5 Canadian couples still
got on board. At the next stop, at 14th Street, 7 men and 8 women got off,
and a group of 18 Japanese people got on. Next, at Christopher Street, a
group of 25 children with 2 chaperons got on board, and two families of
5 people each got off the boat. At Battery Park half of all the passengers
got off, and interestingly, nobody wanted to get on. This way the boat arrived
to its last stop with 66 passengers. With how many passengers did the boat
leave from 42nd Street?
A.634. You can fill up a baby pool with
thirty 5-liter buckets of water. Adam is always in a rush, so he spills
a third of every full bucket on his way from the water faucet to the pool.
How many turns does it take for him to fill up the pool?
A.635. Last summer, Adam and his friends
entered the sailing competition with 5 solo boats. There were a total of
432 sailboats in the race. They did very well because all 5 boats finished
in the top 10. Laslie's and George's boats finished after Zoe's. Adam's
boat was faster than Mario's but slower than Zoe's. Laslie did beat Adam,
and George finished behind Mario. What was the relative order of the 5 friends?
A.636. There are so many animals hiding
in the high grass on the side of a lake. One day Susan saw a few wild ducks,
turtles and water snakes with a total of 16 heads and 28 legs. How many
ducks, turtles and water snakes could she possibly see?
A.637. Fiona collects $10-, $20-, and $50-bills
in her saving box because she loves to buy unique dolls for her collection.
Last time she paid $640 from her box using and equal number of these 3 kinds
of bills. How many $50-bills did she have in her box before paying if she
had 5 of them left after she paid?
A.638. Olga keeps her 96 dolls in 4 boxes.
One day, she put half of the dolls from the first box into the second box,
3 dolls from the third box into the fourth box, and this way she had an
equal number of dolls in each box. How many dolls did she have originally
in each box?
A.639. In a toy store, they sell two kinds
of toy bears: one that can cry, and one that cannot. There are half as many
crying bears than silent bears. The total number of bears is just as many
more than 240 as many less than 240 crying bears there are.
A.640. Tamara bought an 8-piece puzzle
in a 10x10 square box, and now she wants to put then back into the box.
Can you help her?
Top view of the pieces: 
Top view of the box: 
Please, send your solutions to: