‘I look at it this way, sir. If you make it public, you’re playing A B C’s game. That’s what he wants—publicity—notoriety. That’s what he’s out after. I’m right, aren’t I, doctor? He wants to make a splash.’

Thompson nodded.

The Assistant Commissioner said thoughtfully:

‘So you’re for balking him. Refusing him the publicity he’s hankering after. What about you, M. Poirot?’

Poirot did not speak for a minute. When he did it was with an air of choosing his words carefully.

‘It is difficult for me, Sir Lionel,’ he said. ‘I am, as you might say, an interested party. The challenge was sent to me. If I say “Suppress that fact—do not make it public,” may it not be thought that it is my vanity that speaks? That I am afraid for my reputation? It is difficult! To speak out—to tell all—that has its advantages. It is, at least, a warning…On the other hand, I am as convinced as Inspector Crome that it is what the murderer wants us to do.’

‘H’m!’ said the Assistant Commissioner, rubbing his chin. He looked across at Dr Thompson. ‘Suppose we refuse our lunatic the satisfaction of the publicity he craves. What’s he likely to do?’

‘Commit another crime,’ said the doctor promptly.

‘Force your hand.’

‘And if we splash the thing about in headlines. Then what’s his reaction?’

‘Same answer. One way you feed his megalomania, the other you balk it. The result’s the same. Another crime.’

‘What do you say, M. Poirot?’

‘I agree with Dr Thompson.’

‘A cleft stick—eh? How many crimes do you think this—lunatic has in mind?’

Dr Thompson looked across at Poirot.

‘Looks like A to Z,’ he said cheerfully.

‘Of course,’ he went on, ‘he won’t get there. Not nearly. You’ll have him by the heels long before that. Interesting to know how he’d have dealt with the letter X.’ He recalled himself guiltily from this purely enjoyable speculation. ‘But you’ll have him long before that. G or H, let’s say.’

The Assistant Commissioner struck the table with his fist.

‘My God, are you telling me we’re going to have five more murders?’

‘It won’t be as much as that, sir,’ said Inspector Crome. ‘Trust me.’

He spoke with confidence.

‘Which letter of the alphabet do you place it at, inspector?’ asked Poirot.

There was a slight ironic note in his voice. Crome, I thought, looked at him with a tinge of dislike adulterating the usual calm superiority.

‘Might get him next time, M. Poirot. At any rate, I’d guarantee to get him by the time he gets to F.’

He turned to the Assistant Commissioner.

‘I think I’ve got the psychology of the case fairly clear. Dr Thompson will correct me if I’m wrong. I take it that every time A B C brings a crime off, his self-confidence increases about a hundred per cent. Every time he feels “I’m clever—they can’t catch me!” he becomes so over-weeningly confident that he also becomes careless. He exaggerates his own cleverness and everyone else’s stupidity. Very soon he’d be hardly bothering to take any precautions at all. That’s right, isn’t it, doctor?’