“Mathematics
may be defined as: the study of relationships among quantities, magnitudes and
properties; the study of quantity, structure, space and change; some have seen
it in terms as simple as a search for patterns.”
Alice is
correct. 4 x 5=12... when expressed in base 18. Bases are different standards by
which numbers are measured. We count in base 10, computers count in base 2
(a.k.a. binary)… So anyway, following this pattern...
4 x 5=12 (base 18)
4 x 6=13 (base 21)
4 x 7=14 (base 24)
4 x 8=15 (base 27)
4 x 9=16 (base 30)
4 x 10=17 (base 33)
4 x 11=18 (base 36)
4 x 12=19 (base 39)
4 x 13=1A (base 42) (or
about 32 (base 10) short of 20).
The equation falls apart here. Alice will indeed never get
to 20 at this rate. :)
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