A case (Number II)

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Holmes
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A case (Number II)

Post by Holmes »

Hello folks!

Here´s a second case for your brains.

Have fun and Enjoy!

----------------- o -----------------

" Blood and Sand "

  Yesterday, Sargent Bergonias received a call saying that the millionare Lincoln Justin has been murdered.
  He arrived at Lincoln Dustin´s mansion more or less at 7 o´clock and found Lincoln Dustin lying on the library´s floor with a knife stabbed in his heart and the blood was spread all around the floor.
  The Sargent searched there and there, then he started his questioning. Nobody had a strong alibi. When he started asking the butler, he said:" The master had a really ordered life. Every day at midday, he would start a sand clock(Note: the sand clock was beside the victim) and it would finish twelve hours later.(12 o´clock p.m) When it finished, he would go to sleep. "
  Sargent Bergonias didin´t find anything suspiocious, but that day at night the butler called him:
"Sir! Today sand clock didn´t finish at 12, but at 3!"
  The Sargent went to the Police Headquaters and gave this information to the Chief Inspector Jason. The Inspector reasoned that Mr. Dustin had turned around the sand clock to give information of the crime time.
  Suddenly he said:
"You were at the mansion at 7 o´clock more or less, so, the murederer could be you."
Bergonias was deep in his thoughts when he said:
" The sand clock! Now I remember, I was looking the sand clock when i found that it was on top a paper. I thought it was suspicious, so I took the sand clock and turned it around. "
" When did that happen? " the Inspector asked.
" At 7h 30m. "
" My friend! That saves you!" the Inspector finished.

Questions: why did the Inspector suspect the Sargent? and when did the crime happen then?
Last edited by Holmes on February 4th, 2009, 8:02 am, edited 1 time in total.
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Re: A case (Number II)

Post by ayw »

The Inspector suspected the Sargent because, if the victim turned the sand clock around to indicate the time of the murder, and the Sargent hadn't turned around the sand clock, the crime must have occurred at 7:30pm at which time the Sargent was at the mansion.

If what the Sargent says is all true (i.e. he turned the sand clock around at around 7pm), and if the victim turned the sand clock around to indicate the time of the murder, then the crime occurred at 5:30pm.
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Re: A case (Number II)

Post by Holmes »

Oh My... That was really quick!

Well done.
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Re: A case (Number II)

Post by ayw »

Not as quick as the Inspector  :)
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Re: A case (Number II)

Post by sstimson »

question for the great detectives. Is a sand clock like the ones o seen . a lot of sand starts at the top and though a narrow funnel enters the bottom. If so then unless the clock was turned sideways the clock would keep running until all the sand entered the bottom. also say the clock was turned at  seven as in it had been running for seven hours then you turn it over and it will take another seven hours to stop. the clock would stop at two not three unless it takes a hour to turn it over. so how much sand was in the top bay when the killing happened and at seven?

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Last edited by sstimson on February 4th, 2009, 1:03 am, edited 1 time in total.
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Re: A case (Number II)

Post by Holmes »

I think I made a typing mistake. The Sargeant should say:
"At Half - past seven!." and not "At seven!".

Excuse me for my error.
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Re: A case (Number II)

Post by ayw »

Wait, wait... I assumed the Sargent turned the sand clock around at 7pm, rather than 7.30pm. If the Sargent turned the sand clock around at 7:30, then the murder must have taken place at 6pm.

Measuring all times in hours (h) from noon, let x be the time of the murder, and y be the time between murder and 7.30pm, when the Sargent turned the sand clock around. So, x+y=7.5h. y is half the time gained by turning the sand clock around twice, that is, y=1/2*(3am-midnight)=1.5h. Therefore x=6h, so the crime occurred at 6pm.

In this case, there is an easier line of thought still. Lets assume the victim did not turn the sand clock around; only the Sargent did, at 7:30pm. Then the sand clock would end at 3am, which it in fact did. Thus, the victim's act of turning the sand clock did not have an effect on the total duration of the sand clock. The only time this is possible is at 6pm when the top and bottom halves of the sand clock contain equal amounts of sand.

This brings about the possibility that the victim never used the sand clock as a "dying message". The murderer may have placed the sand clock near the victim without turning it around to create a false "dying message" and an alibi. In that case, I find the Inspector quite suspicious...
Last edited by ayw on February 4th, 2009, 9:44 am, edited 1 time in total.
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Re: A case (Number II)

Post by Holmes »

I´ve never thought of that, to be honest, I was rather confused when I read for the first time the case, but what you say is correct, it´s reasonable.
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Re: A case (Number II)

Post by sstimson »

The clock stopped at 3am right? The Guy said he turned it at 7pm. Well from 7pm ( to make this a little more simple ) to 3am is eight hours if you top number below stand for the time it would take the clock to stop ( as in 12 means 12 hours ) and the bottom the time it has been. 6/6 means the clock ran for six hours and has six hours to go. Anyway at 7pm the clock would be 4/8 before the turn and 8/4 after.the clock started at  12pm ( 12/0 ). If the clock had not been turned , then at 7pm the clock should have been 5/7 but it was 4/8. That alone is proof the clock must have been turned at least twice. The clock could not have been turned at 6pm because it would not have shown the second turn ( 6/6 before and 6/6 after ). The clock was likely indeed turned at 5:30 (6.5/5.5 before ad 5.5/6.5 after). That would make the sand time to be 4/8 needed to get the clock right for the 7pm turning.

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Re: A case (Number II)

Post by ayw »

sstimson, that is correct and consistent with my conclusions.

If the Sargent turned the sand clock around at 7pm then the clock must have been turned around at least one more time, otherwise, like you said, the clock wouldn't have lasted until 3am. There is no reason the murderer would turn the clock around and place it next to the victim, so it must have been the victim who turned the clock around. So, in this case, the murder occurred at 5:30pm.

If the Sargent turned the clock around at 7:30pm then the murder occurred at 6pm if the victim did turn the clock around at 6pm. However, in this case we cannot differentiate between the outcome of the sand clock having or not having been turned around by the victim (because in either case the clock would have ended at 3am). Since we cannot be sure that the victim turned the clock around, the time of the crime remains undetermined.

Holmes, could you double check the time the Sargent turned the clock around? And thanks for this puzzle and particularly for the typo, which made it interesting beyond the arithmetics.
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Re: A case (Number II)

Post by Holmes »

Yup, I checked again and it´s 7 o´clock.

I´m glad you liked it.  :D
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Re: A case (Number II)

Post by sstimson »

This is just for Fun But. Questions:

1) The Police arrive at 7:00pm. Why did the Police not see Sargent turn the clock if he turned it at 7:00pm? ( Yes Sargent is the police but normally they come which an assistant and maybe a tech. )
2) If Sargent did turn the clock, why do it when the Police are there? Why not just ask the Police to turn the clock? ( he said he saw a paper but we are never told more about the paper. What was on it. Was it Important? )

I believe the investigation would take between 30 minutes to an hour. After all the Clock needs to be turned only once.

Just a thought. The Clock was not turned by the victim or killer and was only turned by Sargent at 7:30pm, the right time for the 15 hours the clock needed to run. (12am to 3am is 15 hours ). It so then the murder happened any time between 12:00a to 7:00p

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Last edited by sstimson on February 6th, 2009, 2:36 pm, edited 1 time in total.
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