Logic Puzzle 10 - Loyd's Clock
ฝัง
- เผยแพร่เมื่อ 29 ก.ย. 2024
- Comments temporarily turned off as I'm using this for a course.
Logic Puzzle 10 - Loyd's Clock
You wake up to find yourself isolated in a room. The room is padded and there is nothing to read. There is, however, an old clock on the wall. You leap to try take it down, perhaps you can disassemble it and use its parts to escape. But, alas, you cannot reach it. After several weeks in solitary confinement, you recall stories of people going insane from being isolated for too long with nothing to do. You wonder if this will happen to you.
One day, while staring at the clock, you begin to hallucinate. You imagine the clock being transforming into a cake. The clock still looks like a clock but its consistency is that of a clock. The next day, you suffer the same hallucination, but this time you imagine you have two friends with you. While you have been imprisoned for what seems like months now, you have not lost your manners. As you stare at the clock, you consider how you might cut the cake for your new friends. At first, you imagine how you would cut it into three equal portions, but then you wonder how you might cut the cake into three sections so that *the sums of the numbers of the pieces of the cake are equal*. This is easy enough. You would slice the cake as follows:
- The first piece contains XI, XII, I, II = 26
- The second piece contains IX, X, III, IV = 26
- The third piece contains V, VI, VII, VIII = 26
This little mental exercise has bought you another day of sanity. Maybe if you can hold out one more day, your jailors will come to the conclusion that they have wrongly imprisoned you.
The next day, you have the same hallucination but this time you have three friends rather than two. At first, you imagine how you might cut the clock-cake into four equal pieces. This, of course, is rather simple. But then you consider whether it is possible to divide the cake into four sections so that the *sums of the numbers contained in the pieces of the cake are equal*. You feel that if you can solve this problem, you can keep your sanity for just one more day and perhaps tomorrow you will be set free.
The question then is "how do you divide the clock-cake into four sections so that the sums of the numbers in the sections of cake are equal?" If you can answer this question, then I'm sure you can keep your sanity another day.
*** A HINT
Small Hint: Add the numbers on the clock and then divide by 4. This should give you a result that suggests you cannot solve this puzzle in a straightforward way.
*** SOURCES
The images are mostly from Stable Diffusion, all with the prompt of being in the style of Hanno Karlhuber. Surprisingly, I couldn't find a clean, copyright free image of the clock so I made my own. You can use the one I made:
drive.google.c...
The closing song is "Grandfather Clock" by Henry Clay Work. The recording is performed by the "Music for the Nation" singers: staff members from the Library of Congress. As such, it is in public domain. For details, see here: www.loc.gov/it...
Most importantly! The puzzle was created by Sam Loyd (the thumbnail is a 1909 negative of him, Library of Congress). One statement of the puzzle is in the May 1926 issue of Popular Science Monthly, the solution can be found in the June 1926 issue.
__________________________________________
🔴 SUBSCRIBE to my channel for more videos: goo.gl/ukVPLo
➡️ Twitter: / davidagler
🌐 Handouts: www.davidagler.com
Channel Membership Link: / @logicphilosophy
__________________________________________
🎥 Equipment I Use & Like 🎥
► Lights - Neewer 1350W 24x24 Light: amzn.to/3tgJduo
► Microphone - Blue Yeti USB Mic: amzn.to/3vyUbN9
► Microphone Arm - Neewer Microphone Stand: amzn.to/2Rif9kI
► Camera - I use the Canon EOS M50 but don't recommend it.
Note these are US Amazon Affiliate links. I may earn a small commission from this website.
God's in his heaven --
All's right with the world!
__________________________________________
omgggggggggg took me 10 mins to figure out I needed to cut the numbers up - like instead of XI its X separately and I separately. Great question. I was wondering how I could evenly separate 19.5 since it ain't a whole number
LOL! I was in the same boat! Kept thinking I didn't know how to do basic math.
IS IT CAKE? :D
No, the cake is a lie. ;)
LOL. I watched the first season of that show. Strangely mesmerizing!
@@LogicPhilosophy Its a cake! :D
I've got the answer! Hell, I thought I couldn't do it.
So, first of all 78 doesn't good if to sum all the numbers, 'cause 78/4 cannot be divided as an integer. What about the numbers as IX or VI? These can be cut into two, for instance "I/X" or "V/I". That idea of cutting numbers came to me, when I blindedly wanted to divide everything into the 19 (I firstly thought I could do this). So, one number helps us to solve it - this is IX. Because if we use them separately, we can achieve 80. And 80/4 is a good one. So, what we need to do:
a) we take IX and cut it into two I/X, and take a X
b) then we round the next XI and VIII + I (from the previous)
c) then XII + VII + (I from IV below, that is also should be cut into "I/V")
d) the rest part is also sum to XX
Absolutely genius! It took me forever to figure this out. It requires creative thinking rather than raw deductive power! Per your (c), you can also just use XII, I and VII instead of XII, VII and the I from VI. On a side note, I tried to see if you could cut it into five equal parts (introducing another hallucination) but couldn't get it to work. Not sure if there is an answer to that.
On another side note, when I asked ChatGPT to try to solve the puzzle involving only three parts, here is what it said:
"Here's one possible way to divide the clock into three parts:
Part 1: XII (12) - I (1) - XI (11) - II (2) - X (10)
Part 2: III (3) - IX (9) - IV (4) - VIII (8)
Part 3: V (5) - VII (7) - VI (6)
Let's calculate the sums for each part:
Part 1: 12 + 1 + 11 + 2 + 10 = 36
Part 2: 3 + 9 + 4 + 8 = 24
Part 3: 5 + 7 + 6 = 18
In this distribution, we have three parts with sums of 36, 24, and 18, respectively. Although they are not exactly equal, they are as close as possible using the given set of Roman numerals on the clock face."
LOL!
@@LogicPhilosophy Oh, I didn't use that chat. (I don't like robots.)
Do thank you also for providing this example! I must say you - this is not just a riddle for me. When I was a very young kid (I don't remember how old) something happened (I also don't remember it) and this made me very sad. I thought then, what if I couldn't go anywhere, or couldn't move, what should I do? - I thought that I must find the way out if such things occurred. And a thought visited me that at least I could keep staring at the wall (if a wall was nearby) trying to find there 'a little/tiny world'. So, briefly say - to find something in the small area. That is why when I saw the riddle you presented, I couldn't even stop watching; that rusty psychological mechanism of mine (gosh, I sound like a writer :) ) came alive. It was not just a question for me; no, that was something as more, than just a challenge.
By the way, I took a name for the channel, but I didn't know there was yours. Sorry for that. I use it for my students.
Good luck to you! Greeting from Kharkiv, Ukraine! 💙💛