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Broad Topics > Information and Communications Technology > Calculators

### 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. . . .

### Triangle Incircle Iteration

##### Age 14 to 16 Challenge Level:

Keep constructing triangles in the incircle of the previous triangle. What happens?

##### Age 5 to 16

Nowadays the calculator is very familiar to many of us. What did people do to save time working out more difficult problems before the calculator existed?