The penultimate chamber separating Harry and Hermione from the Philosopher’s Stone is a logic puzzle designed by Professor Snape. Here’s an edition of the extract from the book with a mathematical twist, starting with Harry entering the sixth chamber:
He pulled open the next door, both of them hardly daring to look at what came next – but there was nothing very frightening in here, just a table with seven differently shaped bottles standing on it in a line.They stepped over the threshold and immediately a fire sprang up behind them in the doorway. It wasn’t ordinary fire either; it was purple. At the same instant, black flames shot up in the doorway leading onwards. They were trapped.
‘Look!’ Hermione seized a roll of paper lying next to the bottles. Harry looked over her shoulder to read it:
Danger lies before you, while safety lies behind,
Two of us will help you, whichever you would find.
One among us seven will let you move ahead,
Another will transport the drinker back instead,
Two among our number hold only nettle wine,
Three of us are killers, waiting hidden in line.
Choose, unless you wish to stay here for evermore,
To help you in your choice, we give you these clues four:
First, observe the labels we’ve provided as a guide;
The bottles bear the numbers one to seven on the side.
Second, take the number found on either vintage white,
Sep’rately subtract that which thwarts flames as dark as night,
And that which sends you back; multiply these diff’rences –
For either of the nettle wines, three’s what the answer is.
Third, work out the sum of those that shield you from the fire,
Divide by one of the number that will cause you to expire.
Now subtract one, and keep that answer fixed within your mind.
Next take the potion which will let you pass the flames behind.
Subtract its number from that of the poison said before,
Then square; the answers are identical, no less, no more.
Fourth, the number of the potion that will take you back
Is less than that on the potion that takes you through the black.
Hermione let out a great sigh and Harry, amazed, saw that she was smiling, the very last thing he felt like doing.
‘Brilliant‘, said Hermione. ‘This isn’t magic – it’s maths – a puzzle. A lot of the greatest wizards haven’t got a GCSE in maths, they’d be stuck here for ever.’
‘But so will we, won’t we?’
‘Of course not’, said Hermione, ‘Everything we need is here on this paper. Seven bottles: three are poison; two are wine; one will get us safely through the black fire and one will get us back through the purple.’
‘But how do we know which to drink?’
‘Give me a minute.’
Question: identify which of the bottles are poisoned, which are nettle wine, which one will protect Harry and Hermione from the black flames ahead and which one will protect them from the purple flames behind