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166

NAW 5/1 nr. 2 juni 2000 Problemen

Pr oblemen

|

Pr oblem Section

Solutions to the problems in this section can be sent to the editor — preferably by e-mail. The most elegant solutions will be published in a later issue. Readers are invited to submit gener- al mathematical problems. Unless the problem is still open, a valid solution should be included.

Editor:

R.J. Fokkink

Technische Universiteit Delft Faculteit Wiskunde P.O. Box 5036 2600 GA Delft The Netherlands r.j.fokkink@its.tudelft.nl

Problem 1

Eleven journalists have their own bit of slander. They possess special telephones that allow three men to communicate with each other. How many calls are needed to inform everyone of everyone else’s information?

Problem 2

Construct a countable, compact subset of the plane, not contained in a line, that intersects no line in 2 points.

Problem 3

Define a

n

, for n0 by a

0

= 3, a

1

= 0, a

2

= 2 and a

n+3

=

an

+

an+1

for all n ≥ 0. Show

that p |

ap

for every prime number p.

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