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Yoneko had no idea what the receptionist must be thinking. She felt embarrassed, and after making a few hasty apologies, withdrew without bothering to take that so important gas bill with her.

It was some days later, when Miss Munekata gassed herself, that the master key was discovered to have been switched. As this was just the latest such event, the receptionists (neither wishing to take any blame) professed total ignorance of how it had come about. Such, at least, was Yoneko’s interpretation of their silence.

About a week after Yoneko Kimura took the master key, a meeting of the residents’ committee was called. The loss of the key was high on the agenda.

During those seven days, Yoneko had been awaiting her chance to get into Chikako Ueda’s room but, just as normal, Chikako never seemed to go out at all. It appeared that the one exception to this rule was her weekly expedition to the grocer’s, where she would stock up with tinned foods and other durables. How she passed the remainder of her time alone in her room remained a mystery.

It had seemed unlikely that there would be any call for the master key to be used in that short period and so its loss would not have been discovered but for the accident on the second floor. A strong smell of gas was detected outside Miss Munekata’s room, and in the ensuing confusion the theft became known. Now Yoneko could only wait and let matters take their own course.

It appeared that Miss Munekata had gone to sleep leaving the gas stove on, and somehow the flame had been extinguished. One of her neighbours had got up to go to the toilet in the middle of the night, and had noticed the smell of gas exuding from the fanlight window above Toyoko Munekata’s room. It was fortunate that the discovery was made so early, thus avoiding a fatal accident.

Miss Kimura was aroused from her bed in the front office and, rubbing the sleep from her eyes, tried repeatedly to open Miss Munekata’s door with the master key. Needless to say, it did not work, but it took some time for Miss Kimura to realise that this was not due to some failure on her own part, and she spent several minutes reinserting the key in the lock and rattling it to and fro. At last she gave up, and the fire brigade was called. An ambulance with two acrobatic firemen on board arrived in a twinkling; one of them climbed onto a chair and squirmed through the fanlight until he could reach and remove the key from the lock inside. They got into Toyoko Munekata’s room and removed her unconscious body into the open air. She was still breathing faintly and so her life was saved.

If that had been all there was to it, there need have been no further repercussions. However, when they opened the window to air the room, a strong breeze blew in, disturbing the papers on the desk and eventually scattering them all over the place.

The residents had heard how precious the manuscript was, and so several of them entered the room and hastily retrieved the scattered papers. As they did so, they could not help noticing the peculiar mathematical formulae and symbols—triangles, circles, and childish doodles, and even obscene phrases—which made up the text. Rumours swiftly spread around the apartment block, to the effect that Toyoko’s great work was no more than a sham, and that she was touched in the head.

When Yoneko heard this, she was horrified to think that her theft of the master key had nearly brought about the death of a fellow resident. Furthermore, her action had indirectly led to Toyoko Munekata becoming a laughing stock, so that her continued occupancy of the apartment block was imperilled. She felt that Toyoko’s daily labours on the manuscripts of her dead husband were similar in many ways to her own daily letters to her former pupils. And so she could not bring herself to join the chorus of scorn directed towards Toyoko.

‘Just think of it,’ said her fellow committee member. ‘All circles and triangles and crosses.’ She was a school teacher, and had long been resentful of Toyoko’s superior manner. ‘She told us that unlike us she was engaged on a real work of scholarship! Well, that wind certainly showed her up.’

‘But we can’t imagine that her late husband’s research consisted only of such things,’ interrupted Yoneko, springing to Toyoko’s defence. ‘I can’t pretend to be an authority on higher mathematics, but I have heard that once you get to the philosophical level things are not as simple as they appear. I once read somewhere that to a mathematician a circle, or a wheel, say, is not perfectly round at all but is made up of an infinite number of angles.’ She was echoing the thesis she had heard from an enthusiastic young mathematician years ago in the school common room.

‘That’s true,’ agreed the first-floor representative, who worked in a museum. ‘My late husband was a professor of classical Greek. He used to write down all sorts of words and compose vocabularies in those funny letters; it looked more like a childish game than the work of a grown man.’

The committee was assembled for a meeting in the drawing room on the first floor. This room was rarely used and was in consequence dusty and had a mouldy smell. They sat around a large table, on top of which was placed a kettle, teacups and small cakes wrapped in cellophane.

The meeting had been called for six. It was now ten past, but the chairman had not yet arrived. She was a highly skilled and very experienced shorthand secretary who worked at the local council, taking the minutes, and was one of the most highly paid residents in the building. She was very public-spirited, and had served as chairman of the residents’ representative committee without a break for the last five years. The system was that one representative was elected for each floor for a full term of one year, and a further representative was elected for a term of three months. The chairman was also specially elected once a year, making a total of eleven members on the committee. However, at most meetings four or five members would be absent on other business, so the average attendance was about five or six plus the chairman.

The agenda for this specially called meeting consisted of two items, one of them being the perennial problem of cat messes. But the second topic was of much greater interest, and so there was an unusually high attendance, only two of the members being unable to come.

The item of particular concern was the planned movement of the whole building, which had been announced some six months before. Work was due to begin in just one more week.

The door swung open with a crash and a stout female figure came in cautiously as if expecting to find the space too narrow to squeeze through. It was the chairman, Miss Yoko Tanikawa; she was wearing a jacket of masculine cut and had a briefcase under her arm.

‘Sorry to keep you waiting! I had to clarify a few lastminute points about the move, which is on the agenda.’

She sat down at the head of the table and opened her case, producing various documents which she placed in orderly piles on the table.

‘Well, as you all know, they’ll get started on the move from next week. However, there are just one or two problems which need to be kept in mind. For instance, there’s the noise, which will be pretty troublesome. Then there’ll be all the dust—they’re digging out all the foundations, you see. However, taking the broad view, let us not forget that this is being done for the public good. It’s all part of the overall city plan for road-widening, and it is incumbent on all of us to cooperate and to put up with the inconvenience. However, there are limits—just because it is necessary to move the building does not in my view mean that we have to put up with workmen wandering in and out and disturbing our privacy. I would remind you all of how insecure we feel now that the master key has once more vanished. These apartments were founded with the intention of preserving the modesty and so enhancing the status of working women. That one little key was the guarantor of these aims, but in the wrong hands it becomes a threat. In such circumstances, locked doors lose their meaning!’