Junior Mathematical Enrichment Programme
Problem Set 1
1.
The natural numbers 1, 2,3...are written
down in succession. What digit is the 2000th to be written down?
2.
Which of the first 1000 positive integers
are divisible by 2, 3, 4 and 5?
3.
Two cyclists, 20 km apart start toward
each other along a straight road, each cycling at a steady 10 km/hour. A bird
released by one of the cyclists, flies at 20 m/hr until it reaches the
second cyclist. It turns immediately, and flies back until it meets the first,
and continues to repeat this process until the two cyclists meet. What is the
total distance flown by the bird? (Not much calculation needed - it can be done
in a few seconds if you think about it in the right way.)
4.
Two thefts of money had occurred on a
cruise ship, and the ship's detective was baffled.
A news reporter on board had reported details to his
paper, but was not allowed by the detective to give the actual
amounts involved.
So the reporter cabled NEED
NEW
STORY
The editor, realizing that the line below NEW was
significant and knowing that the larger amount stolen was all in $5 notes, was
able to discover the exact amount stolen. Can you? (Assume that different
letters represent different numbers).
5. You throw two ordinary dice, and count the
total. What total are you most likely to find and what is the probability of
getting this total?
Development Band resources have
been produced by the nzamt at each level from year 4 to year 10. Follow the
link to find out more http://nzamt.org.nz/images/stories/pdf/dev_band_manual.pdf
