ABACUS International Math Challenge
for
3rd and 4th graders
April, 2001
Please, note my new e-mail address
on the bottom of this page!
A.249. Can the sum of five consecutive
positive whole numbers be 2001?
A.250. If 2 cats can catch 2 mice in 2
hours, how many mice can 4 cats catch in 4 hours? (Assume that they hunt
with the same effectiveness.)
A.251. Kathryn and Carl are in a ski race.
They begin on the start ramp then ski around each of 17 gates and then head
for the finish line. The 17 gates before the finish line are each
spaced 50 meters apart from start to finish. Kathryn begins skiing
her race, downhill at 10 kilometers per hour. Carl starts 30 seconds
later, skiing at 20 kilometers per hour. Can he catch Kathryn before
she crosses the finish line? If so, where will he pass her?
by Carl Dawson, New York
A.252. What 2-digit number is three times
the sum of its digits?
by Lucky from Alhambra, Illinois
A.253. You have 48 identical cubes. How
many different rectangular based solid columns can you build if you have
to use every cube for every column?
A.254. There are 25 animals on a field.
There are three times as many cows as horses, and twice as many sheep as
pigs. Not every horse was the same color. How many of each kind of animal
are there on this field?
A.255. Arnold Schoenberg, the great 20th
century composer, invented the so-called "12-tone" method of composition
whereby all 12 notes of a chromatic scale (that is C, C#, D, D#, E, F, F#,
G, G#, A, A# and B) are organized into a musical "row." According
to his method, we are not allowed to repeat any pitches until we have first
used up all 12. Mr. Schoenberg would like to know in how many different
ways these 12 pitches can be arranged under the condition that the C and
C# are always separated from each other by at least one other note, and
do not occupy neither the beginning nor the end of the row.
by Patrick Dornian, Canada
A.256. There are a few matches in a matchbox.
If you double the matches in it and then take 8 matches out of the box,
after this you double the number of matches in the box again and then take
8 matches out of the box, and finally, you do the whole thing again for
the third time, you will have no matches in the box. How many matches did
you have in the box at the beginning?
Please, send your solutions to: