ABACUS International Math Challenge
for
3rd and 4th graders
March, 1999
A.113. I got 1526 from 1222 the following
way: 12+1+2=15, and 22+2+2=26. Which number would give you 1998 this way?
A.114. Four girls, Anne, Beatrix, Cecilia,
and Dori, sang songs at graduation last year. Every song was sung by three
of them and the fourth girl accompanied them on the piano. Anne sang the
most songs, a total of 8 of them. Dori sang the least, only five times.
How many songs did the girls sing?
A.115. Three kids, Izzy, Busy and Dizzy,
got into the final of a running race. In the final there was a tie, but
only in one place. How many different ways could the racers get to the finish
line in the final?
A.116. "How many bananas did you bring?"
- asked Judy from her Mom. Her mom said: " A third of the bananas is
3 less than the half of them." How many bananas did she bring home?
A.117. We painted every side of a cube
to either red or blue. How many different ways can you do it if two cubes
are considered to be the same if one can be rotated into the position of
the other.
A.118. Replace the # signs with the digits
0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, using all of the only once, so that the
addition is true. Make sure no number starts with a zero. Try to find more
solutions.
A.119. When a sleeper woke up in the middle
of the night and checked his clock, it showed 3 o'clock, but it was stopped.
He started the clock again and went back to sleep. When he woke up in the
morning a nearby tower clock was tolling seven times. He checked his clock,
but it showed 6 o'clock. What time was it when he woke up at night?
A.120. Draw stars in 7 fields of a 4x4
square so that you would not be able to pick two rows and two columns containing
all 7 selected fields.
Please, send your solutions to: