'Four, if Harry Keogh had taken it.'
'Oh?' Jamieson wasn't convinced. But he was impressed, at least. 'All right,' he said, 'let's assume you're right about the maths side of it. And in fact you are right that the test is a measure of basic intelligence rather than knowledge assimilated parrot-fashion. So what about the other subjects? According to these reports Keogh is a habitual failure in just about any subject you care to mention! Bottom of his class in many of them.'
Hannant sighed, nodded, said: 'Look, I'm sorry I've wasted your time on this one. Anyway, the question hardly arises since he didn't sit the exam in the first place. It's just that I feel it's a shame, that's all. I think the kid has potential.'
'Tell you what,' said Jamieson, coming round his desk and moving towards the door with his hand on Hannant's shoulder. 'Send him to see me during the afternoon. I'll have a word with him, see what I think. No, wait — maybe I can be a little more constructive than that. Instinctive or intuitive mathematician, is he? Very well — '
He returned to his desk, took a pen and quickly scribbled something on a blank sheet of A4. There you go,' he said. 'See what he makes of that. Let him work at it through the lunch break. If he comes up with an answer, then I'll see him and we'll see how we go from there.'
Hannant took the sheet of A4 and went out into the corridor, closing the door behind him. He looked at what the head had written, shook his head in disappointment. He folded the sheet and pocketed it, then took it out again, opened it and stared at it. On the other hand… maybe it was exactly the sort of thing Keogh could handle. Hannant was sure that he could do it — with a bit of thought and a spot of trial and error — but if Keogh could work it out, then they'd be on to something. His case for the boy would be proven. In the event Keogh failed, then Hannant would simply stop worrying about him. There were other kids who were equally deserving of his attention, he was sure…
At 1:30 p.m. sharp Hannant knocked on Jamieson's door, was through it on the instant the head called him in. Jamieson himself was just back from lunch, hardly settled down. He stood up as Hannant crossed the floor of his study, shook out the folds of the A4 and handed it to him.
'I did as you suggested,' Hannant told the head, breathlessly. 'This is Keogh's solution.'
The headmaster quickly scanned the scribbled text of his original problem:
Magic Square: A square is divided into 16 equal, smaller squares. Each
small square contains a number, 1 to 16 inclusive. Arrange them so that the sum of each of the four lines and each of the four columns, and the diagonals, is one and the same number.
The answer, in pencil — including what looked like a false start — had been drawn beneath the question and was signed Harry Keogh:
Jamieson stared at it, stared harder, opened his mouth to speak but said nothing. Hannant could see him rapidly adding up the columns, lines, diagonals — could almost hear his brain ticking over. 'This is… very good,' Jamieson finally said.
'It's better than that,' Hannant told him. 'It's perfect!'
The head blinked at him. 'Perfect, George? But all magic squares are perfect. That's the lure of them. That's their magic!'
'Yes,' Hannant agreed, 'but there's perfect and there's perfect. You asked for columns, lines, diagonals all total ling the same. He's given you that and far more. The corners total the same. The four squares in the middle total the same. The four blocks of four total the same. Even the opposing middle numbers at the sides come out the same! And if you look closer, that's not the end of it. No, it is perfect.'
Jamieson checked again, frowned for a moment, then smiled delightedly. And finally: 'Where's Keogh now?' 'He's outside. I thought you might like to see him…' Jamieson sighed, sat down at his desk. 'All right, George, let's have your prodigy in, shall we?' Hannant opened the door, called Keogh in. Harry entered nervously, fidgeted where he stood before the head's desk.
'Young Keogh,' said the head, 'Mr. Hannant tells me you've a thing for numbers.' Harry said nothing.
'This magic square, for instance. Now, I've fiddled about with such things — purely for my own amusement, you understand — ever since, oh, since I was about your age. But I don't think I ever came up with a solution as good as this one. It's quite remarkable. Did anyone help you with it?'
Harry looked up, looked straight into Jamieson's eyes. For a moment he looked — scared? Possibly, but in the next moment he went on the defensive. 'No, sir. No one helped me.'
Jamieson nodded. 'I see. So where's your rough work? I mean, one doesn't just guess something as clever as this, does one?'
'No, sir,' said Harry. 'My rough work is there, crossed out.'
Jamieson looked at the paper, scratched his very nearly bald head, glanced at Hannant. Then he stared at Keogh. 'But this is simply a box with the numbers laid in their numerical sequence. I can't see how — '
'Sir,' Harry stopped him, 'it seemed to me that was the logical way to start. When I got that far I could see what needed doing.'
Again the head and the maths teacher exchanged glances.
'Go on, Harry,' said the head, nodding.
'See, sir, if you just write the numbers in, like I did, all the big numbers go to the right and to the bottom. So I asked myself: how can I get half of them over from right to left and half of them from the bottom to the top? And: how can I do both at the same time?'
'That seems… logical' Jamieson scratched his head again. 'So what did you do?'
'Pardon?'
'I said, what — did — you — do, boy!' Jamieson hated having to repeat himself to pupils. They should hang on his every word.
Harry was suddenly pale. He said something but it came out a croak. He coughed and his voice dropped an octave or two. When he spoke again he no longer sounded like a small boy at all. 'It's there in front of you,' he said. 'Can't you see it for yourself?'
Jamieson's eyes bugged and his jaw dropped, but before he could explode Harry added: 'I reversed the diagonals, that's all. It was the obvious answer, the only logical answer. Any other way's a game of chance, trial and error. And hit and miss isn't good enough. Not for me…'
Jamieson stood up, flopped down again, pointed an enraged finger at the door. 'Hannant, get — that — boy — out — of — here! Then come back in and speak to me.'
Hannant grabbed Keogh's arm, dragged him out into the corridor. He had the feeling that if he hadn't physically taken hold of the boy, then Keogh might well have fainted. As it was he propped him up against the wall, hissed 'Wait here!' and left him there looking slightly dazed and sick.
Back inside Jamieson's study, Hannant found the head master soaking sweat from his brow with a large sheet of school blotting paper. He was staring fixedly at Harry's solution and muttering to himself. 'Reversed the diag onals! Hmm! And so he has!' But as Hannant closed the door behind him Jamieson looked up and grinned somewhat feebly. He had obviously regained his self control and continued to dab away at the sweat on his forehead and neck. 'This bloody heat!' he said, waving a limp hand and indicating that Hannant should take a seat.
Hannant, whose shirt was sticking to his back beneath his jacket, said, 'I know. It's murder, isn't it? The school's like a furnace — and it's just as bad for the kids.' He remained standing.
Jamieson saw his meaning and nodded. 'Yes, well that's no excuse for insolence — or arrogance.'
Hannant knew he should keep quiet but couldn't. ' he was being insolent,' he said. 'Thing is, I believe he was simply stating a fact. It was the same when I crossed him yesterday. It seems that as soon as you crowd him he gets his back up. The lad's brilliant — but he'd like to pretend not to be! He does his damnedest to keep it hidden.'