Challenge Answers 2000

Please feel free to email me if you have any queries about these answers, and I will update the page if necessary. My email address is P.M.Strickland@livjm.ac.uk or you can ring me on 0151-231-2274 (answerphone if you ring long enough).

1. The Millipedal Bug.

110 cm.

2. CD Review

a) 10 (one by each composer I had before).
b) 37 (3 Dvorak, 4 Es, and 5 of each of the rest)

3. Cutting corners.

a) 24.5 seconds (25 metres of mowing + 4 turns)
b) 17 seconds (16 metres of mowing + 3 turns)

4. Milly on air?

a) £12 000 as a radio presenter, £15 600 as a pilot.
b) £13 200 as a radio presenter, £30 000 as a pilot.

So even if the starting salary is slightly less, you are much better off with monthly increases than with a yearly increase which is 12 times as large!

5. Ice Star

a) The perimeter will be 576m at stage 3, which is more than double the original.
b) The perimeter will be 768m at stage 4, which is more than treble the original.

The area never gets greater than that of the hexagon drawn by connecting the outside corners of the stage 1 star, and so never even reaches double the area of the original triangle.

Provided a good reason was given we accepted the answer that it never becomes twice or three times the length.

6. Pass down the bus please.

One monthly pass, then two weekly ones, and two monthly passes coming to £125.60.

7. Eeny Meeny

No it doesn't always work, but so long as somebody goes out the first time round, then it will always work for prime numbers of people.

8. Trillenium Bug?

a) 6 times.
b) 6 times.
c) 5 times.
d) 9 times.

This totals to 26 doublings, which certainly will take at least a year. This leaves at least 5 doublings before disaster can strike, which will make at least 32 years. So the answer to the next part is;

e) 1970 + 32 = 2002

On the other hand, we know that doubling a second 5 times gives less than a minute; doubling a minute 5 times gives less than an hour; doubling an hour 4 times gives less than a day; and doubling a day 8 times gives less than a year. This totals 22 doublings from one second to under a year, and leaves 9 more before the bug must hit. This would translate to an answer of

f) 1970 + 512 = 2482

The exact time when the bug would hit is Tuesday January 19th 2038, at 03:14:08.