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Indices and Surds
Climbing Powers
Age 16 to 18
Challenge Level 
2\wedge 3\wedge 4 could be (2^3)^4 or 2^{(3^4)}. Does it make any difference? For both definitions, which is bigger: r\wedge r\wedge r\wedge r\dots where the powers of r go on for ever, or (r^r)^r, where r is \sqrt{2}?
Irrational Arithmagons
Age 16 to 18
Challenge Level
Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?