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Polycircles
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
Nim
Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.
Equilateral Areas
ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.
Age 14 to 16 Challenge Level:
The terms $a_1, a_2, a_3,...\ a_n,...\ $ of a sequence are given
by: $$a_n =\frac{1+a_{n-1}}{a_{n-2}}.$$ Investigate the sequences
you get when you choose your own first two terms. Make a conjecture
about the behaviour of these sequences. Can you prove your
conjecture? Investigate the sequences.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.