ABACUS International Math Challenge
for
3rd and 4th graders
December, 2005
You have to go through 7 rooms in order to get to the fortune chamber
of a magician. Each room contains a math problem, and solving that problem
allows you to advance into the next room.
The problem of the 1st room:
A.513. Find all those 2-digit numbers in
which the sum of the digits is odd, and they are divisible by the sum of
their digits.
The problem of the 2nd room:
A.514. Fill in the empty spaces by using
either 2, 5, or 10, so that the sum of the numbers in each column and each
row is 22.
The problem of the 3rd room:
A.515. The wonder plant brings three flowers
every week: a red, a yellow and a white. It loses a different color flower
by the end of each week: red on the first week, yellow on the second, white
on the third week, and so on. How many yellow flowers are there on the plant
at the end of the 10th week?
The problem of the 4th room:
A.516. Draw 5 straight lines on a piece
of paper. How many intersecting points can they have the most?
The problem of the 5th room:
A.517. Starting from the top left field
of 1, you may move to the right or down by one field each time to get to
the bottom right field of 9. What are the greatest and the smallest possible
sums of the numbers along the way? How many different ways can you get 116
as the sum?
The problem of the 6th room:
A.518. The pages of the Magic Book containing
all the magic words are numbered. They started to print the page numbers
only on the third page writing the number 3 on it. How many pages are there
in the book if they used a total of 1690 digits for all the page numbers?
The problem of the 7th room:
A.519. If you solve this problem correctly
you receive 100 000 golden coins in the fortune chamber. How long does it
take you to count your prize if it takes you one second to count each coin?
A.520. There were many brave people who
wanted to get to the fortune chamber of the magician by trying to solve
the problems in the 7 rooms. A third of them, however, did not even get
to the 2nd room. 26 people did not make it from the 2nd to the 3rd room.
Only half of the people who got there could answer the question in the 3rd
room. Everybody solved the problem in the 4th room, but only a tenth of
those people managed to set foot in the 6th room. Here 4 people failed to
solve the problem, so only one person got to the 7th room, who solved that
problem successfully, also, and got the prize. How many people tried to
get the prize?
Please, send your solutions to: