BS: Brain Games

Subject: BS: Brain Games
From: Donuel
Date: 29 Apr 22 - 07:29 PM

Picture a digital clock next to a mirror so the time is seen in the mirror and the clock.
The question is how many times in 24 hours does the mirror time exactly match the clock time?
example: 11:11 would appear twice

Subject: RE: BS: Brain Games
From: Helen
Date: 29 Apr 22 - 07:45 PM

Well, brain games are good for staving off dementia, so I'll have to think about this puzzle and get back to you Donuel.

The interesting thing is that 2 would be the mirror image of 5, so....

Hmm! I'll have to think about this one.

Subject: RE: BS: Brain Games
From: Nigel Parsons
Date: 29 Apr 22 - 07:47 PM

11:11 would only appear twice in 24 hours if you have a 12 hour clock. In which case you might just as well ask about occurrences within a 12 hour period!

Subject: RE: BS: Brain Games
From: Donuel
Date: 29 Apr 22 - 07:54 PM

rules say 24 hours. One solution is to stare at the clocks for 24 hours
Helen may be one of those dyslexic genius'

Subject: RE: BS: Brain Games
From: Helen
Date: 29 Apr 22 - 08:02 PM

Is it in the 24 hour format of 11.11 pm is shown as 23.11 or are we doing the 12 hour and 12 hour times?

The 24 hour format gives a whole lot of other options e.g. 00:32 (am) is 23:00 (pm).

Dyslexic and genius - I'll claim both titles, but I'm overreaching on the genius bit.

Subject: RE: BS: Brain Games
From: Helen
Date: 29 Apr 22 - 08:04 PM

Oh no, wrong example:

The number has to look backwards. 00:55 is 22:00.

Subject: RE: BS: Brain Games
From: Rapparee
Date: 29 Apr 22 - 08:25 PM

I use the Unix time stamp and convert it in my head.

Subject: RE: BS: Brain Games
From: Helen
Date: 29 Apr 22 - 08:44 PM

Well, my first guess is 132 for 24 hour time format.

You can only use the numbers which look the same or like another number in mirror image, so 0,1,2,5 and 8 but 8 is a problem because you can't go over the 24 hour limit and for the same reason the 2 on the end of a time e.g. 11:02 cannot be used for the times over 24 hours because it would reverse to 50:11.

(Do I have to reveal that I am an MsExcel nerd, or can I just let you think I did it in my head?)

Subject: RE: BS: Brain Games
From: Helen
Date: 30 Apr 22 - 12:56 AM

Nope, I just realised that I did it wrong.

I was counting all the times which could be read right way around and in the mirror but it has to match the mirror image. What I calculated was the number of possible times which can be read forwards or mirror image.

Like 15:21 or 12:51.

Back to the drawing board!

Subject: RE: BS: Brain Games
From: Dave the Gnome
Date: 30 Apr 22 - 01:59 AM

Yea, rules need to be clarified. We know it is a 24 hour period but is the clock using 12 or 24 hour format? In 12, as has been pointed out 11:11 would happen twice, as would 10:01 and 00:00. In 24 hour format those times would only happen once.

Subject: RE: BS: Brain Games
From: Helen
Date: 30 Apr 22 - 03:39 AM

The figure I gave earlier of 132 was the possible times which could be read in a mirror on a 12 hour format clock, so there would be more possible numbers if I looked at the 13:00 up to 23:59 numbers.

I still might be wrong, but oh well, nothing ventured etc

00:00        
01:10        
05:20
and its reverse 02:50
15:21
and its reverse 12:51
21:15        
20:05        
10:01

Subject: RE: BS: Brain Games
From: Jon Freeman
Date: 30 Apr 22 - 10:21 AM

Not Excel, Helen but something that might be trivial enough for me to have a stab at although my head spins round looking at the numbers and I’m easily confused. I might have got this python attempt wrong, especially with your estimates, and I’m sure it could be done far better. I’ve included 8 as it reads the same both ways but I don’t think there is an instance where it can be reversed:

swaps = ['0', '1', '5', 'x', 'x', '2', 'x', 'x', '8', 'x']
  x = 0
  for hr in range(0, 24):
      for min in range(0, 60): 
          orig = str(hr).zfill(2) + str(min).zfill(2)
          rev = ""
          for i in reversed(range(0, 4)):
              num = int (orig[i])
              if swaps[num] == 'x':
                  rev = ""
                  break
              else:
                  rev = rev + swaps[num]
          if len(rev) == 4:
              revhr = rev[0:2]
              revmin = rev[2:4]
              if int (revhr) < 24 and int (revmin) < 60:
                  print (orig[0:2] + ":" + orig[2:4] + " - " + revhr + ":" + revmin)
                  x = x + 1
  print(x)

00:00 - 00:00
00:01 - 10:00
00:05 - 20:00
00:10 - 01:00
00:11 - 11:00
00:15 - 21:00
00:20 - 05:00
00:21 - 15:00
00:50 - 02:00
00:51 - 12:00
00:55 - 22:00
01:00 - 00:10
01:01 - 10:10
01:05 - 20:10
01:10 - 01:10
01:11 - 11:10
01:15 - 21:10
01:20 - 05:10
01:21 - 15:10
01:50 - 02:10
01:51 - 12:10
01:55 - 22:10
02:00 - 00:50
02:01 - 10:50
02:05 - 20:50
02:10 - 01:50
02:11 - 11:50
02:15 - 21:50
02:20 - 05:50
02:21 - 15:50
02:50 - 02:50
02:51 - 12:50
02:55 - 22:50
05:00 - 00:20
05:01 - 10:20
05:05 - 20:20
05:10 - 01:20
05:11 - 11:20
05:15 - 21:20
05:20 - 05:20
05:21 - 15:20
05:50 - 02:20
05:51 - 12:20
05:55 - 22:20
10:00 - 00:01
10:01 - 10:01
10:05 - 20:01
10:10 - 01:01
10:11 - 11:01
10:15 - 21:01
10:20 - 05:01
10:21 - 15:01
10:50 - 02:01
10:51 - 12:01
10:55 - 22:01
11:00 - 00:11
11:01 - 10:11
11:05 - 20:11
11:10 - 01:11
11:11 - 11:11
11:15 - 21:11
11:20 - 05:11
11:21 - 15:11
11:50 - 02:11
11:51 - 12:11
11:55 - 22:11
12:00 - 00:51
12:01 - 10:51
12:05 - 20:51
12:10 - 01:51
12:11 - 11:51
12:15 - 21:51
12:20 - 05:51
12:21 - 15:51
12:50 - 02:51
12:51 - 12:51
12:55 - 22:51
15:00 - 00:21
15:01 - 10:21
15:05 - 20:21
15:10 - 01:21
15:11 - 11:21
15:15 - 21:21
15:20 - 05:21
15:21 - 15:21
15:50 - 02:21
15:51 - 12:21
15:55 - 22:21
20:00 - 00:05
20:01 - 10:05
20:05 - 20:05
20:10 - 01:05
20:11 - 11:05
20:15 - 21:05
20:20 - 05:05
20:21 - 15:05
20:50 - 02:05
20:51 - 12:05
20:55 - 22:05
21:00 - 00:15
21:01 - 10:15
21:05 - 20:15
21:10 - 01:15
21:11 - 11:15
21:15 - 21:15
21:20 - 05:15
21:21 - 15:15
21:50 - 02:15
21:51 - 12:15
21:55 - 22:15
22:00 - 00:55
22:01 - 10:55
22:05 - 20:55
22:10 - 01:55
22:11 - 11:55
22:15 - 21:55
22:20 - 05:55
22:21 - 15:55
22:50 - 02:55
22:51 - 12:55
22:55 - 22:55
121

Subject: RE: BS: Brain Games
From: Jon Freeman
Date: 30 Apr 22 - 10:21 AM

And here’s my attempt with values changed for a 12 hr clock:

01:00 - 00:10
01:01 - 10:10
01:10 - 01:10
01:11 - 11:10
01:20 - 05:10
01:50 - 02:10
01:51 - 12:10
02:00 - 00:50
02:01 - 10:50
02:10 - 01:50
02:11 - 11:50
02:20 - 05:50
02:50 - 02:50
02:51 - 12:50
05:00 - 00:20
05:01 - 10:20
05:10 - 01:20
05:11 - 11:20
05:20 - 05:20
05:50 - 02:20
05:51 - 12:20
10:00 - 00:01
10:01 - 10:01
10:10 - 01:01
10:11 - 11:01
10:20 - 05:01
10:50 - 02:01
10:51 - 12:01
11:00 - 00:11
11:01 - 10:11
11:10 - 01:11
11:11 - 11:11
11:20 - 05:11
11:50 - 02:11
11:51 - 12:11
12:00 - 00:51
12:01 - 10:51
12:10 - 01:51
12:11 - 11:51
12:20 - 05:51
12:50 - 02:51
12:51 - 12:51
42

Subject: RE: BS: Brain Games
From: Stanron
Date: 30 Apr 22 - 11:11 AM

AS far as I can see the initial time has to mirror itself either side of the colon before the reflected time can a mirror time.

The only numbers that mirror other numbers or themselves are

0
1
2
5
8

so

00:00
01:10
02:20
10:01
12:51
15:21
20:02
22:22
25:52

Note 52:25 is an invalid time as is anything using 8.

That gives me nine times.

Have I missed any?

Subject: RE: BS: Brain Games
From: Jon Freeman
Date: 30 Apr 22 - 12:23 PM

I must admit, I'm very confused as to what is wanted. Using Helen's later ideas (I think...), I get:

12hr:
00:00 - 00:00
01:10 - 01:10
02:50 - 02:50
05:20 - 05:20
10:01 - 10:01
11:11 - 11:11
12:51 - 12:51
7

24hr:
00:00 - 00:00
01:10 - 01:10
02:50 - 02:50
05:20 - 05:20
10:01 - 10:01
11:11 - 11:11
12:51 - 12:51
15:21 - 15:21
20:05 - 20:05
21:15 - 21:15
22:55 - 22:55
11

Subject: RE: BS: Brain Games
From: Donuel
Date: 30 Apr 22 - 12:45 PM

Jon, I want your brain and maybe a liver.

Subject: RE: BS: Brain Games
From: Helen
Date: 30 Apr 22 - 02:37 PM

Well done, Jon. I forgot to add 11:11 to my list i.e. the example Donuel gave in the original post, but totally missed 22:55 from my list. Just checked my Excel page and yes, there it was but I forgot to add it to my list.

Subject: RE: BS: Brain Games
From: Helen
Date: 30 Apr 22 - 02:52 PM

I have a book called The Lateral Logician by Paul Sloane & Des MacHale.

When I was teaching workplace communications at an adult learning college I used to throw one of these puzzles at the class members at the end of a lesson because it encouraged questioning, searching for facts and information, using logic and working together to find the answer. They could ask Yes/No questions.

This is one of the first puzzles in the book, in the easy section.

1.2 Bombs Away
"One night during the Second World War, an allied bomber was on a mission over Germany. The plane was in perfect condition and everything on it worked properly. When it had reached its target, the pilot ordered the bomb doors opened. They opened. He then ordered the bombs released. They were released. But the bombs did not fall from the plane. Why should this be so?"

Subject: RE: BS: Brain Games
From: Stanron
Date: 30 Apr 22 - 03:04 PM

Was he dropping Flares as spotters or leading lights?

Subject: RE: BS: Brain Games
From: Helen
Date: 30 Apr 22 - 03:21 PM

No. None of those.

Subject: RE: BS: Brain Games
From: MaJoC the Filk
Date: 30 Apr 22 - 03:57 PM

I'll see what the Management makes of that one, but I'm thinking she'll ask: Were the bombs actually loaded?

Subject: RE: BS: Brain Games
From: MaJoC the Filk
Date: 30 Apr 22 - 03:58 PM

--- Ah! was the plane upside down :-) ?

Subject: RE: BS: Brain Games
From: Helen
Date: 30 Apr 22 - 04:02 PM

Yes, the bombs were loaded.

And yes, too clever! The plane was upside down. It was night time and back in the WWII era they wouldn't have had an upside-down warning dial.

Subject: RE: BS: Brain Games
From: Helen
Date: 30 Apr 22 - 04:05 PM

There are hundreds more of those puzzles in the book I have but also a lot are out there on the internet. Search for "lateral thinking puzzles".

Or I can post some more here.

Subject: RE: BS: Brain Games
From: Helen
Date: 30 Apr 22 - 07:29 PM

One of my ways of keeping my brain active is playing a computer game called Spelunky .

I have the rebooted version from 2012 called Spelunky HD.

Spelunky wiki fandom page

The reason it is so good for the brain is that every time a level opens it is randomised, so no cruising along is allowed because you never know what happens next.

I used to play Rayman and the sequels but after seeing the challenges of each level it became a bit easy to disengage the brain because I knew that at this point, I have to do this, at the next point, I have to do that.

In Spelunky everything is a surprise, and only the basic gameplay functions stay the same.

A warning, though: it's addictive. Just one more go, just one more go.

Subject: RE: BS: Brain Games
From: Dave the Gnome
Date: 01 May 22 - 03:45 AM

The question was not which times can be mirrored but "how many times in 24 hours does the mirror time exactly match the clock time?" So only Jon's latter entries fit!

Subject: RE: BS: Brain Games
From: Helen
Date: 01 May 22 - 05:26 AM

Yes, but Dave the Gnome, we were waiting for Donuel to clarify whether he was asking for 24 hour time i.e. 00:00 to 23:59, or 00:00 to 11:59 and then the same repeated for the second period of 12 hours.

Donuel appears to be AWOL so we'll await the adjudicator's decision. LOL

Subject: RE: BS: Brain Games
From: Jon Freeman
Date: 01 May 22 - 05:35 AM

Helen, i fairness to Dtg, I'll agree that my first attempt was addressing the wrong question but I'd got things a bit confused yesterday...

Anyway, I don't think a stab at how many times the reading could be mirrored does any harm. And, at least you and I agree on a possible solution to the real question.

Subject: RE: BS: Brain Games
From: Dave the Gnome
Date: 01 May 22 - 05:41 AM

...but 5 does not mirror as 2! It inverts though. The only numbers that mirror correctly are 0, 1 and 8. In the constraints of the original question I think that the only times that are the same as the real time when viewed in a mirror are

0000
0110
1001 and
1111

The only times an analogue clock with no numbers on is correct in a mirror are 12, 12:30, 6, 6:30, 3:15, and 9:45

If you ignore the length of the fingers you could have other combinations so an analogue clock gives more scope :-)

Subject: RE: BS: Brain Games
From: Dave the Gnome
Date: 01 May 22 - 05:45 AM

Helen, the question is when is the time in a mirror the right time so, as only 0 and 1 can be mirrored correctly, the 12 or 24 hour format is irrelevant. 8 can be mirrored of course but no time has 80 or 81 in hours or minutes.

Subject: RE: BS: Brain Games
From: Dave the Gnome
Date: 01 May 22 - 05:49 AM

Oh, sorry, ignore the comment about other combinations on an analogue clock. I've had another think and don't think there can be any others. Can there?

Subject: RE: BS: Brain Games
From: Dave the Gnome
Date: 01 May 22 - 05:52 AM

And sorry again, Helen! Given the constraints, the 4 times when a clock is correct in a mirror happen twice in 12 hour format so it does matter.

Subject: RE: BS: Brain Games
From: Jon Freeman
Date: 01 May 22 - 06:02 AM

Well Dtg, by my eyes, if I enter 52 on my desk calculator and view that in a mirror, I see 52. It will invert too in which case, I see 25 both ways.

I suppose a question could be raised over the type of display the digital clock uses? That calculator uses 7 segment LCD.

Subject: RE: BS: Brain Games
From: Jon Freeman
Date: 01 May 22 - 06:10 AM

fwiw, if I take 2 and 5 out my program, I get

00:00 - 00:00
01:10 - 01:10
10:01 - 10:01
11:11 - 11:11
4

for the real solution and

00:00 - 00:00
00:01 - 10:00
00:10 - 01:00
00:11 - 11:00
01:00 - 00:10
01:01 - 10:10
01:10 - 01:10
01:11 - 11:10
10:00 - 00:01
10:01 - 10:01
10:10 - 01:01
10:11 - 11:01
11:00 - 00:11
11:01 - 10:11
11:10 - 01:11
11:11 - 11:11
16

for the other attempt.

Subject: RE: BS: Brain Games
From: Helen
Date: 01 May 22 - 07:06 AM

The mirror is next to the clock not above or below it. Left to right mirroring.

"Picture a digital clock next to a mirror so the time is seen in the mirror and the clock."

The format of numbers on a digital clock i.e the "font" created by straight lines, shows a 2 and a 5 using five straight lines in each number. If you view a digital clock version of a 2 in the mirror next to the clock it looks like a 5. The curve on the top right of a 2 and the curve on the bottom right of a 5 are not there. They are straight lines.

Subject: RE: BS: Brain Games
From: Stanron
Date: 01 May 22 - 07:29 AM

That's how I see it too. Back at the start of the 1990s I did a computer maintenance course. One of the things we learned was how to set the digital display on the front of a PC case to show some particular number or another. I forget the exact details now. They were seven segment displays. Four vertical and three horizontal. All digital clocks worked the same way. They were set with jumpers on the inside.

I learned to do this only to find that the technology had moved on and cases no longer used those numbers. Happy days.

Subject: RE: BS: Brain Games
From: Jon Freeman
Date: 01 May 22 - 07:48 AM

Helen, I've just had a look on Amazon for my curiosity. Most digital clocks I found on the first page there use a 7 segment LED or LCD with the straight lines but I did find a couple using a curved font. While I largely agree with you, I'd have to concede the question is open to interpretation.

Subject: RE: BS: Brain Games
From: Donuel
Date: 01 May 22 - 07:57 AM

I am not qualified to adjudicate. I only assumed that AM and PM time would show 4 straight line correct time matches in the mirror. If the : is ignored, there are more matches such as 205. Slanted italic renditions would render 0 matches.

Frankly this was a crazy spin off idea that sub atomic particles don't care if time moves forward or backwards. It appears today they do care:
Now physicists have found proof of one theorized exception to this rule.

"Usually, time is symmetrical for particles, meaning events happen the same way if time progresses forward or backward. For example, a video of two particles colliding and scattering off each other can be played forward or backward, and makes sense either way. (That's not the case for macroscopic objects in the real world. You can spill a glass of milk on the floor, but if time were to move backward, the milk can't pick itself up and fall back into the glass.)

However, physicists thought there might be cases where time wasn't symmetrical for particles either — where certain events worked with time flowing in one direction and not the other. Now, for the first time, they've found proof of this phenomenon.
Researchers working on the BaBar experiment, which ran from 1999 to 2008 at the SLAC National Accelerator Laboratory in California, analyzed nearly 10 years of data from billions of particle collisions. They now report that certain types of particles change into one another much more often in one direction than they do in the reverse, confirming that some particle processes have a preferred direction in time."
Quote: livescience.com

Don't sweat it, its still theoretical junk. Suppose anti matter moves backwards to our time - it looks like our time has more future/past in it than anti matter time because there is more of it..

Subject: RE: BS: Brain Games
From: Dave the Gnome
Date: 01 May 22 - 09:22 AM

Ahhhhh - Didn't spot the 5 and 2 being straight lines! Thanks. My brain has stopped working :-) So, we now have

0000
0110
0250
0520
1001
1111
1251
1521
2005
2115
2255

Anything else?

Subject: RE: BS: Brain Games
From: Jon Freeman
Date: 01 May 22 - 09:31 AM

That agrees with Helen and me.

Subject: RE: BS: Brain Games
From: Dave the Gnome
Date: 01 May 22 - 09:38 AM

That's unusual for me :-D

Subject: RE: BS: Brain Games
From: Donuel
Date: 01 May 22 - 10:48 AM

Thats not unusual for me. You guys found 5 answers while I only saw 4.
Military time excluded.

Subject: RE: BS: Brain Games
From: Helen
Date: 01 May 22 - 03:54 PM

This brain puzzle was harder in practice than it looked. My brain feels a bit fitter than it was a couple of days ago. Well done!

Donuel, is it 5 or 6 without 24 hour time?

01:10, 02:50, 05:20, 10:01, 11:11, 12:51

(assuming that 12:00 is not shown as 00:00)

I like that if you put 1251 and 1521 together you get a palindrome - 12:5115:21.

Subject: RE: BS: Brain Games
From: Helen
Date: 01 May 22 - 05:58 PM

Some more thoughts on the randomised computer game, Spelunky.

Having studied business and management, I find myself thinking about business-type decisions while playing the game. What resources do I have i.e. time, equipment, money, or health/life of the character - if I take a chance on this move will the character suffer or even die? Is it worth using a specific resource in the hope of acquiring another resource or an advantage in the gameplay especially if I don't have definite information about what I'll get out of it? What are the risks and opportunities of specific decisions? If resources are scarce, should I risk them in the hope of gaining an advantage or will I shoot myself in the foot and regret it? How many resources do I need or what pre-planning do I need to do to achieve a foreseeable goal in the future, which is sometimes a level or more ahead in the game? There is a small time-frame on each level so sometimes it's difficult to go back to the beginning of the level, or sometimes there are obstacles preventing that, or not enough resources to do it. Sometimes I strike it lucky and get the best resource, a jet-pack to fly wherever I want, and sometimes I kick myself because then I get over-confident and take unnecessary risks and die.

It's definitely not a mindless game and the randomisation mimics life - and business - so it keeps my synapses firing. :-D

Subject: RE: BS: Brain Games
From: Donuel
Date: 01 May 22 - 07:46 PM

If its 6:40 my clock doesn't display 06:40 so...

Thought experiments are as old fashioned as oil paintings but they still have value. They may appear simple but require a different way of thinking. Albert Eienstien's simplest thought experiments revealed an entirely new way to see gravity and time. trust me they are simple.

Looking at something through the lens of a single discipline is inferior to looking through many disciplines. There is an old saying 'jack of all trades and master of none'. Few if any are masters of all trades. So most of us just do the best we can with deficits, over thinking it and our training/bias.

                   I find complexity that is true but unintuitive is sometimes a warning that I'm looking at an incomplete understanding.
But that too could be wrong since translating a concept into language or math is tricky. :^? More and more I'm being told reality is just a fuzzy probability at its core.
for example;
I'm looking at the recent 'glowing donut' radio telescope composite picture of our black hole Saggitarious A star and they say the black center is not the black hole itself but only its shadow. I'm not sure I get what they mean by 'shadow' although I get that light is being drawn inward. Maybe I get it maybe I don't. Its fuzzy.
























if

Subject: RE: BS: Brain Games
From: Helen
Date: 01 May 22 - 08:26 PM

I tried to read this recent article but I'll have another go and see if it makes some more sense to me:

Time might not exist , according to physicists and philosophers — but that’s okay

Subject: RE: BS: Brain Games
From: Nigel Parsons
Date: 02 May 22 - 09:39 AM

Time is an illusion
Overtime doubly so ;)

Subject: RE: BS: Brain Games
From: MaJoC the Filk
Date: 02 May 22 - 10:26 AM

That explains it, then: When I'm in coding (or worse, debugging) mode at the keyboard, there's no such thing as time .... [sepulchral voice] .... only eternity.

Subject: RE: BS: Brain Games
From: Donuel
Date: 02 May 22 - 11:08 AM

lol Nigel. My pal Al said the first part but the second part is better.

It a poor article Helen. Space-time exists.

Picture this; if you were to RACE away from the face of a noontime clock at the speed of light, when you look at the image of the clock racing along with you it will be frozen at noon no matter how long you travel.
For both you and the image of that clock moving at the speed of light TIME HAS STOPPED. Time will vary, going slower the faster you go until you reach the ultimate speed limit where time stops.

If you can picture that, just know that you can't go the speed of light because you have mass.
Massless things can only go the speed of light.

Time sort of emerges from velocity and distance in space.


Gravity is nearly as easy to picture as an emergent force, But its a longer story.

Subject: RE: BS: Brain Games
From: Helen
Date: 02 May 22 - 05:31 PM

Sorry, Donuel, you are wasting your virtual breath on me by discussing physics etc. It has been 50 years since I left school and even then we never got into the complexities, just the basics. LOL

Back to the original puzzle: the reason I tend to think in 24 hour time mode is because of my last job, dealing every day with hundreds of digital images with date and time identification on them.