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PERNVMERVPYTHAGOREIDESVMTESALPETRAMCARBVM

'Look at this string,' Thomas said, excited. 'Pythagorei – see it? Surely there is meaning here at last.'

'Good, good,' Bacon said. 'You can imagine the variants I explored before I hit on this correct route through the maze. Now all we have to do is find the breaks between the words…'

But Thomas was ahead of him, splitting the line with bold slashes.

And there, for Saladin, the magic happened, a readable sentence emerging from a clamour of nonsense. He was the first to read it aloud: '"By Pythagoras's number take saltpetre, charcoal, sulphur."'

'Almost there,' said Bacon. 'Almost there.'

'But what does it mean?'Joan said.

'Well, Pythagoras's number is obvious. It is six.'

'It is?'

'Six is the perfect number,' said Saladin.

Thomas raised his eyebrows at him. 'And why is it perfect?'

'Because if you take the numbers that divide into it evenly…' Saladin took the chalk now, and wrote out, 1,2,3. 'If you add them up you get six again.' 1+2+3=6.

Bacon smiled. 'Once again you surprise us.'

Saladin felt sheepish. 'Another lucky number for the villagers.'

'In fact there are many perfect numbers,' Bacon said. 'Pythagoras did indeed study them. Twenty-eight is the next one. You see, it is divisible by-'

'Never mind,' Joan said hastily. 'So now we have this: "By one, two, three take saltpetre, charcoal, sulphur."'

'Or,' Bacon said, 'three, two, one. In fact those proportions aren't quite correct, but near enough the range that a little trial and error gives you the right product. The value of experimentation,' he said, smiling.

Saladin was mystified again. 'What product?'

'Why, it's obvious – black powder. Haven't you heard of it? The Chinese have studied it for centuries, we're told. They call it the "fire drug". It's said they found it looking for an elixir of life! I had been hoping to obtain samples via the trade routes opened up by the Mongol empire, in order to verify its properties for myself. Now I can begin to experiment with its very manufacture.'

'The manufacture of what?' Joan demanded. 'What does this stuff do, you infuriating monk?'

He didn't seem insulted. 'Well, if you set fire to it-'

'Yes?'

'It explodes.'