Wednesday, 16 October 2013

Math Extension

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


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