Euler pops up again

STUCK for a gift for a mathematically inclined friend? Feedback recommends the Myriorama (myriorama.notlong.com) - a set of 24 cards cunningly designed so that, placed side-by-side in any order, they form one plausible picture. The Myriorama, which costs just £2.99, is in the style of slightly saucy beach postcards.

The website says there are "an astonishing 1,686,553,615,927,922,354,187,744 possible pictures" to be made." And here, of course, the mathematics comes in. John Woods's first thought on seeing the page was that the number of ways of arranging 24 cards should be 24 factorial - which is written 24! and is 24 × 23 × 22... × 2 × 1.

But 24! is only 620,448,401,733,240,000,000,000. Then Woods realised you don't have to use all the cards, so the number of arrangements you can make is larger. But what really surprised him was the realisation that the number the site reports is (to the nearest whole number) 24! multiplied by Euler's constant e - which keeps popping up all over the place (New Scientist, 21 July 2007, p 38). But why here on a set of seaside postcards?