[ Pobierz całość w formacie PDF ]
a second, but which felt abyssally longer, as if our fates were being weighed by distant judicial
machinery. Then thumps and vibrations signalled the opening of the door.
Simultaneously, the door behind us had opened again. The route out of the Spire was now clear again.
'Forqueray . . .' Childe said.
The Ultra tossed the float-cam into the darkness.
'Well?'
'This is getting a tiny bit monotonous. Another chamber, another door, another set of markings.'
'No booby-traps?'
'Nothing the drone can resolve, which I'm afraid isn't saying much.'
I ll go in this time,' Celestine said. 'No one follow me until I've checked out the problem, understood?'
'Fine by me,' Hirz said, peering back at the escape route.
Celestine stepped into the darkness.
I decided that I was no longer enjoying the illusion of seeing everyone as if we were not wearing suits -
we all looked far too vulnerable, suddenly - and ordered my own to stop editing my visual field to that
extent. The transition was smooth; suits formed around us like thickening auras. Only the helmet parts
remained semi-transparent, so that I could still identify who was who without cumbersome visual tags.
'It's another mathematical puzzle,' Celestine said. 'Still fairly simple. We're not really being stretched
yet.'
'Yeah, well, I'll settle for not being really stretched,' Hirz said.
Childe looked unimpressed. 'Are you certain of the answer?'
'Trust me,' Celestine said. 'It's perfectly safe to enter.'
This time the markings looked more complicated, and at first I feared that Celestine had been over-
confident.
On the left-hand side of the door - extending the height of the frame - was a vertical strip marked by
many equally spaced horizontal grooves, in the manner of a ruler. But some of the cleanly cut grooves
were deeper than the others. On the other side of the door was a similar ruler, but with a different arrange-
ment of deeper grooves, not lining up with any of those on the right.
I stared at the frame for several seconds, thinking the solution would click into my mind; willing
myself back into the problem-solving mode that had once seemed so natural. But the pattern of grooves
refused to snap into any neat mathematical order.
I looked at Childe, seeing no greater comprehension in his face.
'Don't you see it?' Celestine said.
'Not quite,' I said.
'There are ninety-one grooves, Richard.' She spoke with the tone of a teacher who had begun to lose
patience with a tardy pupil. 'Now counting from the bottom, the following grooves are deeper than the
rest: the third, the sixth, the tenth, the fifteenth . . . shall I continue?'
'I think you'd better,' Childe said.
'There are seven other deep grooves, concluding with the ninety-first. You must see it now, surely.
Think geometrically.'
'I am,' I said testily.
'Tell us, Celestine,' Childe said, between what was obviously gritted teeth.
She sighed. 'They're triangular numbers.'
'Fine,' Childe said. 'But I'm not sure I know what a triangular number is.'
Celestine glanced at the ceiling for a moment, as if seeking inspiration. 'Look. Think of a dot, will you?'
'I'm thinking,' Childe said.
'Now surround that dot by six neighbours, all the same distance from each other. Got that?'
'Yes.'
'Now keep on adding dots, extending out in all directions, as far as you can imagine - each dot having
six neighbours.'
'With you so far.'
'You should have something resembling a Chinese chequer board. Now concentrate on a single dot
again, near the middle. Draw a line from it to one of its six neighbours, and then another line to one of the
two dots either side of the neighbour you just chose. Then join the two neighbouring dots. What have you
a got?'
'An equilateral triangle.'
'Good. That's three taken care of. Now imagine that the triangle's sides are twice as long. How many
dots are connected together now?'
Childe answered after only a slight hesitation, 'Six. I think.'
'Yes.' Celestine turned to me. 'Are you following, Richard?'
'More or less . . .' I said, trying to hold the shapes in my head.
'Then we'll continue. If we triple the size of the triangle, we link together nine dots along the sides, with
an additional dot in the middle. That's ten. Continue - with a quadruple-sized triangle - and we hit fifteen.'
She paused, giving us time to catch up. 'There are eight more; up to ninety-one, which has thirteen dots
along each side.'
'The final groove,' I said, accepting for myself that whatever this problem was, Celestine had definitely
understood it.
'But there are only seven deep grooves in that interval,' she continued. 'That means all we have to do is
identify the groove on the right which corresponds to the missing triangular number.'
'All?' Hirz said.
'Look, it's simple. I know the answer, but you don't have to take my word for it. The triangles follow a
simple sequence. If there are N dots in the lower row of the last triangle, the next one will have N plus
one more. Add one to two and you've got three. Add one to two to three, and you've got six. One to two to
three to four, and you've got ten. Then fifteen, then twenty-one . . .' Celestine paused. 'Look, it's senseless
taking my word for it. Graph up a chequerboard display on your suits -Forqueray, can you oblige? - and
start arranging dots in triangular patterns.'
We did. It took quarter of an hour, but after that time we had all - Hirz included - convinced ourselves
by brute force that Celestine was right. The only missing pattern was for the fifty-five-dot case, which
happened to coincide with one of the deep grooves on the right side of the door.
It was obvious, then. That was the one to press.
'I don't like it,' Hirz said. 'I see it now . . . but I didn't see it until it was pointed out to me. What if
there's another pattern none of us are seeing?'
Celestine looked at her coldly. 'There isn't.'
'Look, there's no point arguing,' Childe said. 'Celestine saw it first, but we always knew she would.
Don't feel bad about it, Hirz. You're not here for your mathematical prowess. Nor's Trintignant, nor's
Forqueray.'
'Yeah, well remind me when I can do something useful,' Hirz said.
Then she pushed forward and pressed the groove on the right side of the door.
Progress was smooth and steady for the next five chambers. The problems to be solved grew harder,
but after consultation the solution was never so esoteric that we could not all agree on it. As the
complexity of the tasks increased, so did the area taken up by the frames, but other than that there was no
change in the basic nature of the challenges. We were never forced to proceed more quickly than we
chose, and the Spire always provided a clear route back to the exit every time a doorway had been
traversed. The door immediately behind us would seal only once we had all entered the room where the
current problem lay, which meant that we were able to assess any given problem before committing
ourselves to its solution. To convince ourselves that we were indeed able to leave, we had Hirz go back
the way we had come in. She was able to return to the first room unimpeded - the rear-facing doors
[ Pobierz całość w formacie PDF ]