Can we find a base in which 21 can be divided by 12 without remainder? And why should we? - Because someone said it couldn't be done. They may well have meant that it can't be done if the base is a positive number - and in fact, if you use base (-5) then 21 = 3 x 12 is true.

Which led me to look at some other results in other bases - not recent discoveries, I might add; the keyboard is ready and willing to work, but occasional bursts of lethargy often hit the typist, in particular Nap Attacks as favoured by Garfield.^{(1)}

- 31 = 2 x 13 (base 5)
- 41 = 3 x 14 (base eleven)
- 51 = 3 x 15 (base seven)
- 51 = 4 x 15 (base nineteen)
In tabular form:

**Number****Bases****31****5****41****11****51****7, 19****61****29****71****9, 17, 41****81****13, 55****91****11, 31, 71****T1****23, 89****E1****13, 19, 29, 49**and here are some with 2 as unit-figure **52****8****72****19****82****11****92****34****T2****19****E2****14, 53**and so on ... (to be continued)

Footnote:

^{(1)}No, not the President; the cartoon cat.