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‘Don’t you want to find out who killed him?’ I asked her. Again she shook her head.

‘Yer a wummin yersel’, are ye no’?’ she said, looking at me searchingly. ‘A wife and a mither o’ bairns?’ I nodded. ‘Can ye no’ jist leave it be?’ she asked. ‘Can ye no’ for the love of God jist leave it?’

I was more puzzled than ever. What woman would not want the murder of her husband to be investigated? What woman in the world would not want her husband’s killer to be caught? What did she mean?

‘I can’t leave it, Mrs Dudgeon,’ I said. ‘But I promise that I’ll do my best to keep your private business private.’

She looked at me very shrewdly, almost amused, and said to me: ‘I’d doubt that, madam. If ye kent whit it wis. I doubt you’d do that.’

‘Two more questions,’ I told her. ‘You don’t have to answer but I need to ask. First, what were you doing that night, with the pen and ink?’ She shook her head and gave a short, bleak laugh.

‘Nothin’,’ she said. ‘Runnin’ roun’ the woods like a daftie.’

‘Very well,’ I said. ‘I’m not going to press you. And now this is my last question, I promise. Do you know why, can you tell me why, Robert was going to leave you?’ Her look of incomprehension was quite genuine, I was sure. ‘I know about the ticket,’ I told her, ‘I know it was for your husband alone.’ It took a moment or two for her to understand what I meant and then there was no flush of annoyance or shame, only a tired shake of the head to brush the silliness out of her way.

‘I will find out in the end,’ I said. ‘I must.’

‘Well, if you must you must,’ she said, her tone almost mocking. ‘But it’s no matter to me, madam. It’s no matter at all now.’

I recounted all of this to Alec as we made our way home, trying to give him a flavour of her mood, her strange serenity, even though there was nothing very concrete to which I could pin it.

‘It could just be grief,’ he said, showing me that I had failed. ‘Or maybe she finally got the doctor to prescribe a little something as her sisters were pressing her to do. Very frustrating for us, obviously, but the police will be able to make her talk. So it will come out in the end even if we don’t have the satisfaction of getting our questions answered.’

‘It was just one question she wouldn’t answer,’ I said. ‘About the pen and the ink. She was perfectly honest about the hip flask, I’m sure, and her face answered me more plainly than any words could have on the point of Robert leaving her. Whatever he was up to it wasn’t that.’

‘It must have been,’ said Alec. ‘Nothing else makes sense. Her face must just be better suited for poker than you’re giving it credit for. What about X?’

‘X?’ I said. ‘X leaving her? I’m not with you, darling.’

‘I mean did you ask Mrs Dudgeon about X? Did you ask her who he was? If anyone’s in a position to verify his identity, it must be her. He was in the cart with her.’

I groaned. Somehow, unbelievably, I had forgotten to ask a single thing about that. So there was another question we needed to hand over to Inspector Cruickshank. Unless… I took my foot off the accelerator pedal and the car began to slow gently in the soft dirt of the lane. It was not possible, surely, for all of these questions to be unrelated. X, the ticket to New Zealand, and the pen and ink all had to be connected somehow, and thanks to something that Alec had just that moment said, something which found an echo in my memory, I began to see what it was.

‘In a position to verify his identity,’ I said.

‘Oh Lord,’ said Alec. ‘Did I really just say that? Forgive me. Detecting is one thing, Dan, but please stop me if I start to speak like a newly promoted sergeant with his own bicycle and bell.’

‘It was the chap at Brunwick, Allanson you were quoting,’ I told him. ‘Not that he’s much of a role model either.’ The motor car had ground to a complete halt now and I disengaged the gear and turned to face him.

‘Listen to this,’ I said. ‘What if the ticket wasn’t for Robert Dudgeon at all. What if it was for X. X needed to get away – not the Dudgeons, not Robert – they were just the go-betweens. Perhaps X had a criminal record and would set off alarms if he bought a ticket with his own passport. So Robert planned to do it for him, only when the news broke about the passport office being closed and they realized the clash with the Burry Man it looked as though they were scuppered. Then they had the idea that while Robert was standing in for X, X could stand in for him.

‘Afterwards they were supposed to give him the ticket, in plenty of time for the departure on Tuesday evening, but Robert Dudgeon died and all the paperwork he had on him was stuck in the mortuary. Absolute panic stations. And even when the body and all his belongings were returned, the house was overrun with sisters and X couldn’t get near.’

‘And the pen and ink?’ said Alec.

‘Was to doctor the ticket,’ I said feeling triumphant. ‘To change it from one name – Dudgeon’s – to another – X’s. Only once again, Donald was sitting with the body and one or another of the sisters was sitting with the widow and the day was approaching ever closer. Hence Mrs Dudgeon out wandering in the woods trying to furnish X with what he needed to do the job himself. And hence also her extreme agitation as ten o’clock rolled around on Tuesday night. If X was caught, she would be tried for fraud, or for something anyway, but once he was off British soil and away she was safe.’

‘There’s something in that,’ said Alec. ‘It’s not perfect but…’

‘In what way isn’t it?’ I demanded. ‘It could even explain how Dudgeon died. X killed him. X didn’t trust Dudgeon not to go to the police and confess before X had a chance to get away, and so he killed him. In what way is this not the perfect solution?’

‘Well, doctoring the ticket, for one thing,’ said Alec.

‘The clerk said that as long as they turn up sober -’

‘As long as they turn up with a passport and ticket and sober,’ Alec said. ‘But I’m sure that if the name on the ticket were scratched out and another one scrawled underneath they would have something to say about it.’

‘Well, then, maybe there aren’t names on the ticket,’ I said.

‘Then what would X need the ink for?’ said Alec, which was a very good point. ‘And why would the Dudgeons do this? It must be illegal in some way although I don’t know the name of the crime. Why would they take the risk?’

‘For money?’ I said. ‘If X were paying them? Or threatening them. They might do it out of fear, under duress.’

‘Also,’ said Alec, ‘I don’t really see wh rs Dudgeon would be in a state about registering Robert’s death if what you’re saying now is the answer to the riddle. By Sunday night she had all of his papers back, didn’t she? What was the difficulty?’

I rubbed my nose, trying to think of an answer. There was none as far as I could see, but I was still sure I had hit on something.

‘Perhaps just my saying “birth certificate and passport” together like that when they were so very much in the front of her mind? I don’t know.’ I looked at my watch. ‘But I wonder if there’s time to telephone to Brunwick, Allanson and offer that clerk enormous bribes to let us go in and look through the passenger lists, try to match them up. If we find a name on the passenger list that doesn’t appear on the ticket receipts, that, my darling, will be X.’

‘So it will,’ said Alec. ‘Well, get a move on then, it’s nearly five.’

The clerk did us even better than that, though. When we had been put through to his office by the girl on the main switchboard, far from having to bribe him with favours, he sounded tremendously pleased to hear from us and launched in right away.