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 totalling 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?’