please empty your brain below

This won't take (someone) very long...
85p and 11p
11p and 17p.
66p needs 6 X 11p
85p needs 5 X 17p
96p needs 5 X 17p plus 1 X 11p
£1.29 needs 5 X 17p plus 4 X 11p
...and £1.70 and £2.55 are both multiples of 85p.
No – I'm wrong and Paul’s right. D’oh!
Aha! But my solution needs less stamps and is thus more efficient :-)

66 = 6 x11p
85 = 1 x 85p
96 = 85p and 1x11p
129 = 85p and 4x11p
170 = 2 x 85p
255 = 3 x 85p
*fewer* stamps
Another solution would be 66p and 9p. That would be most efficient if typical users had, say, 50 letters needing 66p and very very few of the other prices.
66p and 9p doesn't work because both of those are multiples of 3 and not all the postage prices are.
They could have got away with just printing penny stamps, and that would also have required larger envelopes, hence increasing revenue.
The best solution NOT involving an 11p stamp would be 16p and 17p stamps. You'd need 15 and 33 stamps respectively to make one of each required denomination, far worse than the 19 (11x11 + 8x85) for Paul's answer.
I agree it's 85p and 11p.

  66 = 11+11+11+11+11+11
  96 = 85+11
  85 = 85
129 = 85+11+11+11+11
170 = 85+85
255 = 85+85+85

...and there must be something intrinsically deliberate about Royal Mail's price structure to have made that particular combination possible.
The last price increase fixed £1.70 as the international rate for anywhere in the world up to varying weights, which was a big change from before. It meant cards to the US under 10g went up from £1.42 last year to £1.70 this year (and I have a lot of US relatives.) £2.55 is for heavier international letters. I'm guessing that £1.70 and £2.55 will remain 2x and 3x 1st class at the next increase. And currently there isn't an 11p stamp - they go 1, 2, 5, 10, 20, 50 and then specific values such as the Xmas set.
If it's still available, printed papers surface post was a lot cheaper last time i used it. It did/does mean posting in October and the card can't contain any lengthy message or enclosure. Indeed when I was originally told about this many years ago the advice was the cards had to be unsealed (flap tucked in).
There is still an international printed papers rate, but it starts at £5.80 for 100g. The flap-tucked-in rates for cards etc were discontinued in 2012 for international mail and 1968 for domestic.










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