The Mystery Clock

For a while, nobody raised any questions. Perhaps it was because they needed to get their heads straight.

“Wait a minute. Isn’t that impossible?” Hikijii broke the silence.

“Indeed, the hall was dark during that time, but Tokizane never had the opportunity to touch the radio-controlled clock.”

To this, almost everyone nodded their heads.

“All of you, of course, are familiar with the principle of the Mystery Clock, aren’t you?”

The question was abrupt, but everyone nodded apart from Junko. Astonishingly, Ota and even the makeup artist were nodding affirmatively.

“The needles of the Mystery Clock are attached to a transparent disk, and the entire disk rotates on gears hidden around the edges,” Natsumi, possibly noticing Junko’s reaction, informed her in a whisper. 

Oh, I didn’t know that. 

Junko was impressed, but then remembered that this was also being filmed and gave a nod as if she had known about this for a long time.

“The radio-controlled clock was like a Mystery Clock with needles floating in mid-air. No one could have touched the clock that night. And yet, the time was manipulated… The time was turned back, perhaps by as much as twelve minutes.”

“Twelve minutes? As mentioned earlier, how can you be so specific about the time?”

Junko questioned, perplexed. Regrettably, she had no idea.

“Please wait a little longer for that explanation,” Enomoto again stammered, “Then, let me explain the specific trick using this clock.”

Enomoto finally held up the large clock he had just taken out.

“First of all, let’s have a look at the structure of the clock. The clock consists of a dial, an hour hand, a minute hand, and a second hand, in that order. Please keep this in mind.”

Isn’t that obvious, Junko thought to herself.

“That radio-controlled clock was not well-received by Mori because it was too plain in design. But that was to be expected. For Tokizane’s scheme, it had to meet a number of conditions.”

Tokizane’s expression seemingly stiffened at Enomoto’s words.

“First, the entire clock had to be a perfect circle with no patterned edges. It should be relatively lightweight. The hands and dial should not be luminous in the dark. If possible, the hands should operate in the shortest possible distance when setting the time by receiving a radio wave. As for the design of the dial, it should have a concentric circle whose radius is close to the length of the hour hand. I suppose it was impossible to find a clock that met these requirements and still had a stylish design.”

“That’s about as much ado to raise someone’s hopes. So how specifically did he do it?”

Kumakura urged him onward as if he were fretting.

“From here on out, it’s all in my imagination. There may be differences in some details, but I am sure I am not mistaken in the major points.”

Enomoto removed the clock’s glass cover and set it down.

“First, Tokizane made two paper dials, color copies of the dials of the real clocks. He said he had two identical radio-controlled clocks, but he most likely purchased another one and disassembled that one for the copy.”

Enomoto now held up two paper dials. One was the same size as the dial, and the other was much smaller.

“The first piece is used to indicate the numbers on the periphery and is the same size as the dial. The glass cover of the clock, which is fixed with screws on the back, has to be removed and the fake dial inserted, but the hands cannot be removed. It is difficult to reattach the hands to ensure that they work properly. For this reason, it is essential to cut a slit in the paper dial, probably in the direction of six o’clock. The slit is taped from the back and the front side is hidden with white paint. Moreover, a bell will be attached to the back side. This dial would be inserted under the hour hand so that it could rotate freely around its axis.”

Enomoto smoothly explained.

“The second dial is inserted between the minute hand and the hour hand. Its size is just right to hide the minute hand, and since there were concentric circles on the original dial, there is no problem if the lines on the edges can be seen.”

Following the explanation, Enomoto inserted the paper dial into the clock and lifted it high so that everyone could see it.

“On the second paper dial, a fake hour hand is stuck on, just like a Mystery Clock. Also, on the back side, there is a small nubble made of paper or glue, which is hooked onto the real hour hand and rotates with its movement of it. The fake hour hand is positioned at an angle of 7 degrees ahead of the real hour hand. Furthermore, there is another nubble attached near the back of the fake hour hand. This leaves the radio-controlled clock with the fake dial, the fake hour hand, and the real long and second hands visible.”

Enomoto cast a fleeting glance at Tokizane. Tokizane, on the other hand, maintained a poker face without making the slightest change.

“Then, the minute hand will be moved forward by twelve minutes.”

There goes the twelve minutes again. This time, I thought I would shut up and wait for the rest of the story, but I still couldn’t figure out what it meant.

“What? He moved it forward this time? Not by delaying it?”

“Yes.”

“But he had to mislead us into assuming it was 9:39 when, in fact, it was 9:51, didn’t he?”

“In order to delay it, it had to be moved forward first,” Enomoto replied cryptically.

“…He moved the time forward? How could he do that?”

Tokizane, who had been listening silently for some time, unexpectedly retorted.

“What? I mean, all you have to do is move the hands normally, right? And the glass cover can be removed, too.”

When Junko asked, Tokizane offered an icy smile.

“Radio-controlled clocks have an internal microcomputer that detects the position of the hands and corrects the time based on standard radio waves, so if you mechanically move the hands, they will not be able to display the correct time.”

“However, his radio-controlled clocks were equipped with a button that allowed the time to be set manually.”

Kawai now expressed his doubts.

“Unfortunately, this radio-controlled clock has neither a knob to turn the hands nor a button to set the time,” Tokizane replied flatly.

“I see. Before tricking people into recognizing the wrong time ー you fooled the clock first, didn’t you?” Motojima said confidently. He was fully aware of the fact that he was being filmed, and he was prepared for the challenge. “What was probably used for that purpose was computer software.”

“Computer software? How can that make a radio-controlled clock operate?

For Junko, this was a gibberish story.

“There is a free software to set the time of radio-controlled clocks using a personal computer. There are two facilities in Japan that transmit standard radio waves to set the time of radio-controlled clocks, but the one that covers all of eastern Japan is the Otakadoya Mountain Standard Radio Transmitting Station in Fukushima Prefecture.”

Motojima shared a piece of surprising knowledge.

“When I was working on a book about the Great East Japan Earthquake, I heard that the Otakadoya Mountain Radio Transmitting Station had temporarily lost its ability to transmit standard radio waves. At that time, there was a person who used this software to accurately set the time on a radio clock.”

“But how do they connect the computer to the clock?”

Junko, who was not well versed in mechanical things, could not even fathom it.

“When you connect a speaker with a headphone jack to the audio output of the computer, then connect headphones with a long cord to the speaker, wind the cord around the speaker, and turn the speaker volume to the maximum, a radio wave is emitted to set the time. If you place a radio-controlled clock by attaching it to the loop of the cord that has been wound around it, it can receive the signal. This would be easier if you used a self-made antenna, but the key thing here is that you can set the radio-controlled clock to any time, not just the correct time, by means of a button on the computer.”

Once more, silence descended.

“I see… I see! That’s all I can think of, too!”

Junko swiftly rode someone’s coattails. Even though she could only understand about half of the explanation, at least she somehow understood that it was possible to manipulate the time on a radio-controlled clock and that it was possible to set the time on a radio-controlled clock.

“Hahaha! Computer software? I have no idea why he would come up with such a bizarre idea. Why do you want to go to such lengths to spread radio waves for no reason?”

Hikijii burst out laughing.

“Are people like you the ones who are being called ‘radio enthusiasts’ these days?”

Motojima was apparently offended by this.

“Do you have a better idea than this then?”

“Isn’t that a given? All you have to do is wait until a favorable moment and remove the batteries. Once the batteries are put back in, the clock will start running from that time.”

Motojima’s mouth hung open. He was unable to follow up on his overly-simple suggestion.

“Apparently, my phrase ‘move the minute hand forward’ was misunderstood. Since the same radio-controlled clock was also in Tokizane’s study, I suspect that he stopped it at a certain time, put in the batteries twelve minutes before that time, and replaced the clock with the one on the wall in the hall.”

Enomoto followed up with a pensive look.

Junko grumbled at Motojima for giving her such an enthusiastic response.

“Now the radio-controlled clock is twelve minutes ahead of the actual time.”

The clock, which Enomoto held in both hands, was tilted so as to rotate it.

“Next, the entire clock is rotated two degrees to the left and secured to the wall so that the indentation at the twelve-minute mark on the real dial is at the top… It’s almost turning sideways now.”

“How did he achieve this?”

Motojima inquired in a low voice.

“With the hook on the wall as a fulcrum, he just needs to attach it somewhere else with adhesive for wallpaper,” Enomoto answered immediately.

It seemed that all the questions that would be posed were within the realm of his expectation.

“Now, here’s what the clock looks like when rotated two degrees to the left.”

When Junko caught sight of the clock in Enomoto’s hand, she felt as if she finally understood what was being attempted.

“The first paper dial rotates freely under the hour hand, and thanks to the weight affixed to the back, it always sets the hour at 6 o’clock down. This means that 12 o’clock is directly above and the dial looks straight. Also, the hour hand on the second paper dial is 72 degrees ahead of the real hour hand, so it will be in the correct position, offsetting the amount of rotation. Finally, the minute hand, which is also offset by the rotation ー is 72 degrees ahead of the actual time, and therefore displays the correct time.”

Enomoto’s subsequent words struck a chilling note in Junko’s heart.

“Cleanliness is really filthiness. At first glance, the time appears to be correct, but the time recognized by the clock is wrong.”

“Hmm. The trick seems to be getting closer and closer to magic,” Hikijii growled.

“What happened then?”

“Tokizane must have switched the radio-controlled clock before the dinner party in the dining room. During that time, the curtains in the hall were kept closed. Those curtains.”

Enomoto pointed to the curtains that hung in the window that opened onto the garden terrace.

“The curtains are made of an unnatural material for hanging here. It is, after all, a curtain used in medical facilities to block electromagnetic waves.”

“Electromagnetic wave shielding curtains? That’s quite intriguing.”

Hikijii moved his wheelchair all the way up to the window to feel the curtains.

“They are stiffer than ordinary curtains. These curtains are probably made of metallic fibers that absorb radio waves. If I hung these curtains in my bedroom, I would be able to sleep in peace. But what in the world do you hang these things for?”

When the question was posed to Tokizane, he looked at Hikujii with a blank expression on his face.

“As you know, there is a large storage battery in the garden. Of course, this is an excessive concern, but it was meant to relieve Reiko, who was extremely concerned about the electromagnetic waves.”

“It is true that when we were relaxing here that evening, Mori was talking about electromagnetic waves. However, Tokizane’s goal was something else entirely.”

Enomoto looked towards the wall of the hall.

“As long as these curtains are closed, the radio clock cannot receive standard radio waves. Hence, the time recognized by the clock is still twelve minutes ahead of the actual time. Of course, to our eyes, it appeared to be displaying the correct time.”

Junko was taken aback.

“The curtains were opened once during the tour, weren’t they?”

“Yes. When Tokizane made a satellite phone call on the garden terrace, he opened the curtains, and they remained open for the rest of the day.”

“The time was, I believe, 9:07,” Motojima said, looking at his notebook.

“Yes. Since then, the radio-controlled clock has been able to receive standard radio waves.”

“Speaking of radio-controlled clocks, I had one at home, too. I think it was around midnight when it received the time… I think it was around 2:00 a.m.”

As if trying to remember, Kawai put his hands to his temples.

“The time of reception varies from model to model. This radio-controlled wall clock should have received the signal twenty-four times a day at thirty minutes past the hour,” Tokizane answered.

“If so, that would mean that the clock received the signal at 9:30 since it was after 9:07. If the clock was correct, that would be true, but the radio clock recognized the time as being twelve minutes ahead of the actual time.”

Enomoto corrected Kawai’s illusion.

“Oh, I see.” 

Junko finally realized this. The time to receive the correct time was the wrong time. It was a mind-boggling story.

“In other words, at 9:18, twelve minutes before 9:30, the radio-controlled wall clock made a reception that it should have made at 9:30. If the clock had any consciousness, it would have been astounded to find itself twelve minutes ahead of its time. It then rushed to correct the time. With most radio-controlled clocks, the hands advance to exactly twelve o’clock and then continue to go around and around until the correct time is reached, but with this model, the hands make the shortest possible movement. So, the minute hand moved leftward by only 12 minutes – 72 degrees. As a result, the time displayed by the clock looks like this.”

Enomoto raised the clock he had brought with him again and tilted it at an angle. It appeared to show approximately 9:06.

“The minute hand seemed to indicate the correct time, because when the time had been moved forward by twelve minutes, the entire clock had been tilted two degrees to the left. However, once the hands return to the correct time position, the minute hand will appear to be delayed by the amount of the tilt of the clock. Despite the apparent delay of twelve minutes, the correct time is in fact being recognized. This is really the saying, ‘Filthiness is cleanliness’.”

“Hold on a minute. What about the hour hand? Wouldn’t that make for an improbable arrangement of the hands?” Hikijii sharply interrupted.

“The clock does not need a minute hand to tell the time, but only an hour hand. In that state, the minute hand would appear to indicate 9:06, but the hour hand would be at 9:18 after receiving a radio signal, and the two-degree leftward tilt of the dial would be offset by the second paper dial so that the time would appear to be at the same 9:18 position after all. Isn’t there a clear discrepancy between the time indicated by the minute hand and the hour hand?”

“But the room was dark at the time, wasn’t it? You couldn’t see the dial.”

Motojima interrupted bluntly. It seemed that he was still bitter about being ridiculed.

“Then what about when the light comes on? Unless the minute hand is treated as if it were twelve minutes behind, the discrepancy between it and the hour hand, which shows the correct time, cannot be resolved.”

“You are right. When the room lightened up, the minute hand was pointing to 9:39, but the actual time was 9:51, and the hour hand was also in that position.”

Enomoto took over Hikijii’s question.

“But the difference in the angle of the hour hand, which corresponds to 12 minutes, is only six degrees – one tick of the second hand. Recall how we usually look at a clock. We read the minutes on the minute hand, but we only check the hour on the hour hand. Nobody ever bothers to check that it is exactly in the right place.”

Then came a silence. Yes, that’s true, Junko thought. In the first place, the hour hand was too short to read the time down to the nearest degree.

Tokizane’s reading of the time went beyond the mere mechanical trickery of the minutes and extended beyond that – to the sheer inaccuracy of human perception.

“I see. I am convinced. Besides, if you think about it, an error of 6 degrees can be divided into two parts. The angle correction on the second piece of paper could be reduced by 3 degrees to 88 degrees. Then the error of the hour hand before and after receiving a radio signal would be minus and plus 3 degrees, respectively. This way, no one would notice it.”

Hikijii nodded in satisfaction, having refined his own plan of attack.

“Somehow, I’m getting confused. Let’s put aside all the details and get to the point,” Motojima said, jotting down information in his notebook with a ballpoint pen. “By 9:18, when the time was corrected, the hall was so dark that the dial on the radio-controlled clock could not be seen. When the room was brightened again, it was actually 9:51, but the time we saw was 9:39, twelve minutes later than the actual time, is that correct?”

“That is correct. He manipulated the time without touching the clock on the wall at all. It was truly a magic trick.”

Enomoto’s tone was easygoing as if he was making idle chit-chat.

“We thought we were here for 49 minutes, from 8:50 to 9:39, to determine the price of the clock, but the radio clock was delayed, so we finished 12 minutes later than we had intended. In truth, from 8:50 to 9:51, sixty-one minutes had elapsed.”

“…But how can a clock alone so perfectly fool a human being’s perception of time? Besides, there were so many of us, let alone a single person. Wouldn’t at least one person among us, someone with excellent intuition, sense something wrong?” Kumakura objected.

“First and foremost, as in the case of magic, a large number of people does not necessarily mean that a person is less likely to be fooled. On the contrary, the presence of people around makes them feel safe, so if they see one person convinced, the rest of the members will be implicated and think that’s the way it’s done. Especially since they would never dream that the time on a radio-controlled clock, which no one has touched, could be altered.”

Perhaps the question was anticipated that Enomoto answered smoothly.

“That’s not all. The criminal ー Tokizane is very ingenious in the way he has applied psychology to our perception of time.”

“Psychology?” Junko wrinkled her brows.

“It is very simple. All of us experience time as passing in a flash when we are having fun or concentrating on something, while time spent in boredom or pain seems to take much longer. This gap in human perception is your area of expertise, isn’t it, Tokizane?”

Tokizane did not answer.

“We were like being dangled by carrots from the tip of our nose at that time, dazzled by the high prize and eager to appraise the clocks with bloodshot eyes. While there was no particular time limit, on the contrary, we never knew when it would come to an end. Because of the rush to find out as soon as possible, the same amount of time would have seemed much shorter than usual. Therefore, no one thought it strange when they were told that it had been 49 minutes when in fact 61 minutes had elapsed.”

Tokizane was not simply playing a trick on the clock; he was manipulating the consciousness of all of them. Tokizane’s words from that night replayed in Junko’s mind.

“That’s exactly what it means when a trick becomes a miracle. A mechanical trick is like a seed or a trick in magic, but it is incomplete by itself. How the trick is presented through words and actions is also crucial. Mechanical tricks, in combination with a psychological performance, can create illusions in the mind at the very beginning.”

“I see. The time we were aware of was delayed by twelve minutes… That’s as far as it goes. If that’s the case, what’s the consequence? What advantage would it bring to the culprit?”

Kumakura closed his eyes and folded his arms, perhaps trying to concentrate.

“It’s plain and simple. It gives him an alibi.”

Enomoto’s lips curved up in a smile.

“Tokizane has an ironclad alibi for the time he was talking on his satellite cell phone – from 9:07 to 9:38. Since he was with everyone before and after that time, it seemed impossible for him to have committed the crime… But what if the time Tokizane appeared in the hall was 9:51 instead of 9:39? The twelve minutes between the end of the call at 9:38 and 9:50 would have been a complete blank. It would mean that there was just barely enough time to go upstairs and poison Mori.”

Junko was shaken to her core.

“But at that time, I could see Tokizane’s return quite clearly through the glass door. He was still talking on his satellite cell phone, but when he finished the call, he opened the sash and came into the hall… Ah, I get it!”

As he spoke, Kawai seemed to realize it himself. Enomoto nodded.

“Yes, that’s right. In fact, the call had ended a long time ago, but it was merely a stinky little play to make it seem like it was just over at the time.”

Enomoto’s tone was uncharacteristically sharp.

“…Wait a minute. Indeed, that was an entertaining deduction. You may have the makings of a mystery writer, Enomoto. But even if I had played such a trick on the radio-controlled clock and rewound the time by twelve minutes, shouldn’t there be a discrepancy in the time afterwards?”

Tokizane began to fight back, but his attitude was somewhat urgent.

“Did you forget? I have been with you all since your return to the hall. It was 9:50 when the discussion to find the culprit began, but from then on, the Grandfather Clock and the flip clock in the dining room were within everyone’s sight, and the passage of time could always be checked, you know. It was 10:47 when we finally came to the conclusion that it was most likely an accident. Subsequently, we all went to the study and started up the PC, and the time that the ringlet had indicated just prior to that time would have been 10:49. After examining Reiko’s unfinished manuscript, we went down to the hall. At this time, the time on the radio clock was 10:55. We experimented to see if the footlights would turn on by tripping the breakers in the garden. And when we started the final game of pointing to who we thought was the culprit, all of us would have looked at the radio clock again. I believe it was 10:58. The game lasted seven minutes, and after the game was over, you returned the wristwatches that had been entrusted to you, and some of us confirmed that the time on the wristwatches and on the radio-controlled clocks was 11:06, a minute later. Furthermore, once the police were present, they must have checked all the clocks in the lodge. You have already confirmed that not only is the time correct, but also that there is no workmanship or anomalies of any kind, right? Yaegashi.”

Having been suddenly asked to speak, Sgt. Yaegashi’s reaction was delayed for a moment.

“Oh… uh, yes. There was nothing unusual on any of the clocks.”

“Exactly what he said,” Tokizane let out a deep breath. “Now you see what this means, don’t you? The radio-controlled clock trick that delayed the time by twelve minutes is nothing more than a theoretical idea. Everyone was checking the time seamlessly by multiple clocks. It is impossible to fool all those eyes.”

“The time was checked seamlessly by multiple clocks. That is the key to the trick in this case,” Enomoto cut him off nonchalantly. “Tokizane created the blank twelve minutes by reducing the time. But then, as you just said, there is a discrepancy with the actual time. To fill the gap, you now stretched the time by twelve minutes.”

“You mean to say that a number of clocks that had been delayed by twelve minutes were made to catch up to the correct time before the police arrived?” Hikijii scratched his head. “Unfortunately, I have no idea how that’s possible.”

“I’ll explain. Let me start by explaining how you set the radio-controlled clock back to the correct time.”

Enomoto glanced around at everyone.