1 Readers' Problems
In this regular feature, you are invited to send us problems for
publication - but with each problem you must send your solution, and,
if the problem is not your own invention, a reference to its source.
A subscription to for 2003 (or equivalent
backcopies) will be awarded to each Reader whose Problem(s) we
publish
in 2002. The best solutions we receive from other readers will be
published under their name. The following Readers'
Problems remain unsolved: 4.3-1, 5.1-1, 5.3-1, 5.3-5, 6.1-3, 6.1-5,
6.1-6, 6.2-1, 6.2-2, 6.2-3.
(By the way, the problem 5.1-1 is not hard, and some copies missed
having the `cancelling strokes': put them in on page 11:
[19/95]=[1\not 9/\not 95]=1/
; [16/64]=[1\not 6/\not64]=1/4.)
- 6.3-1 From Walter Madzimure
FOR FORMS 1-4 ONLY:
Given six identical toothpicks (or matches), it is easy to form an
equilateral triangle with any three. How can you form 4 congruent
equilateral triangles with the six toothpicks?
- 6.3-2 From Owen Sibanda of N.U.S.T.
FOR FORMS 1-4 ONLY:
A car travelled 1000km altogether. It has one spare tyre. The tyres
were rotated at intervals so that each tyre had worn by the same
amount. For how many kilometers had each tyre been used?
- 6.3-3 From Richard Muchovo
FOR FORMS 3 & 4 ONLY:
After the Mutare Agricultural Show, there were a number of cattle,
teachers and pupils assembled near the crush pens. I counted
altogether 68 legs and 20 heads. How many cattle and how many people
were present?
- 6.3-4 From Munyaradzi Mukachana of Victoria High
School
Find the number of integers x such that 1 £ x £ 2004 and x
is relatively prime to 2004.
- 6.3-5 From Munyaradzi Mukachana of Victoria High School
Let n=333¼3 consisting of 100 3's. Consider
the least number N containing only 4's such that
N is divisible by n. How many digits has N?
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