ABACUS International Math Challenge
for
3rd and 4th graders
January, 2005
A.465. There are 147 students in 7 grades
in the school of magicians. Every grade has 2 less students than the grade
below it. How many students are there in the first grade?
A.466.
Three of the second grade students, Abraca, Babraca and Dabraca, collected some
herb leaves for their Magic Drinks class. They collected a total of 11.5 kilograms
leaves. Abraca collected 65 dekagrams more than Babraca, and Dabraca collected
60 dekagrams more than Abraca. How much leaves did each student collect?
A.467. Professor Chiriboo locked up in
his safe those papyrus rolls that contain the most important magic words.
The safe has seven 3-digit-code locks on it. The codes are in a logical
sequence. The students managed to take a quick look at the paper containing
all the codes, but they could remember only the first six codes. They are:
100, 101, 103, 107, 115, 122. What could the last code be?
A.468. "Hurrah! I can do magic and
make gold!" -shouted Professor Alchemicus. He could turn a 3-kg lead
cube into a 2-kg golden cube. Then, if you touch for 2 minutes another 3-kg
lead cube with any of these 2-kg golden cubes you made, you can turn it
into a 2-kg golden cube, too. (One golden cube can turn only one lead cube
into gold at a time.) The whole magic lasts for 15 minutes from the time
the first golden cube was made. How many kg of gold did Professor Alchemicus
make?
A.469. Gossip, the messenger, flew on his
broomstick from the Enchanted Castle to Lake Bottomless. He left at 3:20
pm, and he arrived on the same day at 5:05 pm. The broomstick flew 2 km
every 5 minutes. How far is the lake from the castle if Gossip flew in a
straight line and never stopped?
A.470. In Number Mystery class Professor
Numerous showed his students his new toy. With this machine, which can add,
subtract, multiply and divide, you can change numbers. If you give the machine
8, 10, and 2 (in this order) then the machine changes them to 85. From 4,
15, and 5 it makes 63. From 4, 6, and 2 it makes 27. What is the trick of
the machine? What will it make from 20, 20, and 10?
A.471. The magic cape and the magic hat
together costs $240. The price of the cape is 7/3 of the price of the hat.
How much does each cost?
A.472. Hip, Hop, Hap, and Hoop, the four
silly magical (and not medical) students, one morning in a hurry went to
breakfast so that nobody was wearing his own cape. How many different ways
could they dress up if only those four capes were on the cape hangers?
Please, send your solutions to: