'I see,' said Lewis, unseeing.
'As I say, if we square the first case, and then we square the second case... all we've got to do is to work out the sum of the two squares.'
Lewis looked puzzled. 'I'm not quite following you, sir.'
'Have you heard of 'Pythagorean Triplets'?'
'We did Pythagoras Theorem at school.'
'Exactly. The most famous of all the triplets, that '3, 4, 5': 32 + 42 = 52. Agreed?'
'Agreed,'
'But there are more spectacular examples than that. The Egyptians, for example, knew all about '5961, 6480, 8161.''
'That's good news, sir. I didn't realise you were up things like that.'
Morse looked down at the desk. 'I'm not. I was just reading from the back of this matchbox here.'
Lewis grinned as Morse continued.
'There was this fellow called Fermat, it seems--I called in at home and looked him up. He knew all about 'things like that,' as you put it: square-roots, and cube-roots, and all that sort of stuff.'
'Has he got much to do with us, though--this fellow?'
'Dunno, Lewis. But he was a marvellous man. In one of the books on arithmetic he was studying he wrote some-thing like: 'I've got a truly marvellous demonstration of this proposition which this margin is too narrow to contain.'
Isn't that a wonderful sentence?'
'If you say so, sir.'
'Well, I've worked out the square of three and the square of four and I've added them together and I've come up with--guess what, Lewis!'
'°twenty-five?'
'Much more! You see, this morning I suddenly realised where we've been going wrong in this case. We've been as-suming what we were meant to assume.... No. Let me start again. As you know, I felt pretty certain almost from the beginning that Mc Clure was murdered by Brooks. And I think now, though I can't be certain of course, that Brooks himself was murdered last week. And I know--listen, Lewis!--I now know what Brooks's murderer wanted us to Lewis looked at the Chief Inspector, and saw that not un-comnn, strangely distanced, almost mystical look in the gentian-blue eyes.
'You see, Brooks's body is somewhere where we'll never find it--I feel oddly sure about that. Pushed in a fur- nace, perhaps, or buried under concrete, or left in a rubbish~ dump---'
, 'Waste Reception Area, sir.'
'Wherever, yes. But consider the consequences of the body never being found. We all jump to the same conclu-sion-the conclusion our very intelligent Administrator at the Pitt Rivers jumped to: that there was a direct link tween the murder of Brooks and the theft of the knife, Now, there was a grand deception here. The person who murdered Brooks wanted us to take one fact for grante, and almost--almost!--he succeeded.'
'Or she.'
'Oh, yes. Or she... But as I say the key question this: why was the knife stolen? So let me tell you. Th theft was a great big bluff! For what purpose? To convin{ us that Brooks was murdered after 4:30 P.M. on th Wednesday the seventh, But he wasn't,' asserted Mor slowly. 'He was murdered the day before--he was mu dered on Tuesday the sixth.'
'But he was seen alive on the Wednesday, sir. His wit saw him--Mrs. Stevens saw him--'
'Liars!'
'Both of 'em?'
'Both of them.'
'You mean... you mean they murdered Brooks?'
'That's exactly what I do mean, yes. As I see things, must have been Julia Stevens who supplied the brains, wh somehow arranged the business with the knife. But what-what, Lewis--if Brooks was murdered by another knife--household knife, let's say--a knife just like the on Mc Clure was murdered with, the knife that was found i Daventry Avenue, the knife that was missing from t Brookses' kitchen.'
Lewis shook his head slowly. 'Why all this palave though?'
'Good question. So I'll give you a good answer. To giv the murderer--murderers--watertight alibis for th Wednesday. I sensed something of the sort when I inte J viewed Julia Stevens; and I suddenly knew it this momin when I was interviewing our punk-wonder.' ' 'She's in it, too, you reckon?'
Morse nodded. 'All three of them have been telling t the same thing, really. In effect they've been saying: 'Loot I don't mind being suspected of doing something on Tue,, day--but not on the Wednesday.' They're happy about m having an alibi for the day Brooks was murdered. It wa for the day afterwards--the Wednesday--that for some re son they figured an alibi was vital. And--surprise, sm prise!--they've each of 'em got a beautiful alibi for ther It's been very clever of them--this sort of casual indiffer-ence they've shown for the actual day of the murder, the Tuesday. You see, they all knew they'd be the likely sus-pects, and they've been very gently, very cleverly, pushing us all along in the direction they wanted.'
'All three of them, you think?'
'Yes. They'd all have gladly murdered Brooks, even if they hadn't known he was a murderer himself: the wife
