Thank you for taking the time to create this visually. I'm dyslexic and I think I have dyscalculia. Someone posted the puzzle in a channel and I googled the question and came across your recording.
Ned, thanks for telling me this. So pleased you found this useful. Not all learning styles are the same but when you find what works for you encourage others to help in that way. Some things are just clearer explained visually and I think this is an example. It was a pain to build and film but really quite a lot of fun too! Think it beats a computer simulation hands-down. Good luck with all your studies!
This was actually a rather interesting problem. I realized fairly early on that whether a switch was lit at the end or not would depend on whether the number of its factors was odd or even, but I had never actually realized before that the only numbers with an odd number of factors are also squares!
Middle video prediction: I think it's going to be a hard to predict pattern of off and on. Really appreciate that you made a physical solution, digital models are good but I love the tactile feel and sound of the switch and love seeing people build gadgets. Result: Never expected it to be such a regular squares pattern at the end of it! Math was never a strong point for me, so when you explain these types of iterative problems in a physical way, it makes the concepts a lot easier to understand. So glad I found your channel and thank you for creating all of these fascinating videos.
Thanks, I am so pleased you like the channel and the rather 'obscure' video ideas I like to share. Does make it all worthwhile for a small channel like this! Yes, totally agree with you that a mechanical demonstration (I have been doing these for years in my physics teaching) can really help one understand and visualise a problem. I think a lot of maths teaching could be improved greatly in this area. When I filmed it you only have to miss one switch and you have to start all over again if you forget which one it was! I had sore fingers by the end of this but knew it was worth it! Do keep watching and always good to hear your thoughts!
I also noticed that the ratio of the number of unlit nodes to the place number preceding them is as follows: 1/0.5 • 1/1 • 1/1.5 • 1/2 • 1/2.5 • 1/3 • 1/3.5 • 1/4 • 1/4.444... • 1/∞ ... Arbitrary and unimportant, but it was fun to find out.
Yes, the more you look the more patterns seem to come out of it. You could give some thought to the look of the lights/off ones too if the grid is not 10x10 but some other arrangement such as 4x25 or even 1x100. The solution to which are on and off still remains the same of course!
Yes Tony, there is so much more you can do with this - have you thought of using it as a lit up abacus for example?! Anyway, the switches were quite stiff and my fingers so sore after filming it I think it will remain on the shelf for now!
@@AnthonyFrancisJones I guess my comment was confusing. The first line was my first guess as you requested. I then editted the comment to add my new understanding. Anyway, interesting how that turned out.
Excellent and you did exactly what I did which was worked away at different patterns until one seemed to emerge the winner! Thanks for your comments as ever!
@@Rouverius By the way, I meant to put up any picture for the thumbnail but it turned out I put up a rather 'relevant' one by accident! Glad you still watched the video though!
Yes, David, it is 60. It is a high composite number and the first one out of the 100 switches to have 12 factors. Then 72 and then 84, 90, 96 I believe.
Thank you for taking the time to create this visually. I'm dyslexic and I think I have dyscalculia. Someone posted the puzzle in a channel and I googled the question and came across your recording.
Ned, thanks for telling me this. So pleased you found this useful. Not all learning styles are the same but when you find what works for you encourage others to help in that way. Some things are just clearer explained visually and I think this is an example. It was a pain to build and film but really quite a lot of fun too! Think it beats a computer simulation hands-down. Good luck with all your studies!
This was actually a rather interesting problem. I realized fairly early on that whether a switch was lit at the end or not would depend on whether the number of its factors was odd or even, but I had never actually realized before that the only numbers with an odd number of factors are also squares!
Thanks. Yes it is a very interesting problem and it was fun trying to show it this way. Thanks for sharing your thoughts!
Fun as always Anthony
Something a bit different this time Mark!
Middle video prediction: I think it's going to be a hard to predict pattern of off and on.
Really appreciate that you made a physical solution, digital models are good but I love the tactile feel and sound of the switch and love seeing people build gadgets.
Result: Never expected it to be such a regular squares pattern at the end of it!
Math was never a strong point for me, so when you explain these types of iterative problems in a physical way, it makes the concepts a lot easier to understand. So glad I found your channel and thank you for creating all of these fascinating videos.
Thanks, I am so pleased you like the channel and the rather 'obscure' video ideas I like to share. Does make it all worthwhile for a small channel like this! Yes, totally agree with you that a mechanical demonstration (I have been doing these for years in my physics teaching) can really help one understand and visualise a problem. I think a lot of maths teaching could be improved greatly in this area. When I filmed it you only have to miss one switch and you have to start all over again if you forget which one it was! I had sore fingers by the end of this but knew it was worth it! Do keep watching and always good to hear your thoughts!
I also noticed that the ratio of the number of unlit nodes to the place number preceding them is as follows:
1/0.5 • 1/1 • 1/1.5 • 1/2 • 1/2.5 • 1/3 • 1/3.5 • 1/4 • 1/4.444... • 1/∞ ... Arbitrary and unimportant, but it was fun to find out.
Yes, the more you look the more patterns seem to come out of it. You could give some thought to the look of the lights/off ones too if the grid is not 10x10 but some other arrangement such as 4x25 or even 1x100. The solution to which are on and off still remains the same of course!
Mind twisting how a simple bank of switched lights produces this result. Think of all the input possibilities, on second thoughts don’t 😂 Tony.
Yes Tony, there is so much more you can do with this - have you thought of using it as a lit up abacus for example?! Anyway, the switches were quite stiff and my fingers so sore after filming it I think it will remain on the shelf for now!
Interesting 🙂
Glad you liked it!
All prime numbers?
Edit: Oh! Interesting to see how far each lamp is spaced from each other (2n-1) ... Hope that's not a spoiler. 😅
Good guess! Note that some are divisible by 3 (for example) so cannot be prime numbers! Thanks for watching!
@@AnthonyFrancisJones I guess my comment was confusing. The first line was my first guess as you requested. I then editted the comment to add my new understanding. Anyway, interesting how that turned out.
Excellent and you did exactly what I did which was worked away at different patterns until one seemed to emerge the winner! Thanks for your comments as ever!
@@Rouverius By the way, I meant to put up any picture for the thumbnail but it turned out I put up a rather 'relevant' one by accident! Glad you still watched the video though!
I wondered which switch is switched the most, Gemini said switch 1, Chat GPT said switch 60.
Yes, David, it is 60. It is a high composite number and the first one out of the 100 switches to have 12 factors. Then 72 and then 84, 90, 96 I believe.
1 is obviously not correct, because that is only ever switched on the first turn (because 1 is not divisible by anything except 1).
Yes, it has only one factor.