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Post by johnno56 on Oct 31, 2021 5:25:31 GMT -6
No. I am not suggesting that a game be created.. although that could be a cool project... I have a simple question to ask about the game.
The method of calculating the total moves required to finish the game will depend on two parameters. The number of discs and the amount of time per move.
The formula is: Moves = 2^N-1 where N is the number of discs.
eg: If you have 3 discs then, 2^3-1, would be 7 moves. Let us assume that each move takes about 1 second... The puzzle is solved in 7 seconds.
For 7 discs: 2^7-1 = 127 moves. Just over 2 minutes. For 8 discs: 2^8-1 = 255 moves. 4.25 minutes. For 9 discs: 2^9-1 = 512 moves. Just over 8.5 minutes. For 10 discs: 2^10-1 = 1023 moves. Just over 17 minutes.
Someone asked, "How long would it take to solve the game of 64 discs?"
Breakout your calculators (or RC code). I am feeling generous... I will accept a tolerance of, "To the nearest year".
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Post by n00b on Nov 1, 2021 6:25:38 GMT -6
For 64 discs: 2^64-1 = 18,446,744,073,709,551,615 moves. Just over 584,942,417,355 years.
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Post by johnno56 on Nov 1, 2021 14:05:36 GMT -6
Oh... Too easy... 100% correct! Well done!
Now I have to think of some other puzzle...
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Post by rosy on Nov 2, 2021 1:21:23 GMT -6
I have a simpler riddle: What thickness will the sheet be when folding a piece of paper in half 50 times
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Post by johnno56 on Nov 6, 2021 21:37:02 GMT -6
Oh boy!
Let us assume that the paper is a standard thickness of A4... 0.1mm
Folded 50 times: 2^50 * 10 to convert to millimeters: 1.125899907×10¹⁴mm Divide by 1,000 to to convert to meters: 1.125899907×10¹⁴m Divide by 1,000 to convert to Kilometers: 112589990700 (69960155111 miles)
This should produce a stack of paper that would reach from Earth to just beyond Mars.
But, if you REALLY want to get technical... By hand, you can only fold a piece of paper if half, no more than 7 times...
Did I get it right? Do I win a prize? lol
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Post by rosy on Nov 7, 2021 4:32:41 GMT -6
I don't know ... You were on your way but you made a few mistakes.
1. To convert pages to mm - not * only /, but the final result is somehow good, apart from the roundings.
2. There are different distance metrics, I assume you meant the universal one, the Euclidean one, so: It is impossible to talk about the distance of Earth from Mars, because it is variable. You can give at a given time or, for example, an average, although this can also be counted differently, even if we also take the most popular type of average. So it's better to say that the pile would range from Venus (our closest planet, on average, I think) to the sun. To go from Earth to Sun, the pages had to be a little thicker.
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Post by johnno56 on Nov 7, 2021 5:28:50 GMT -6
Math was never my strong point... *sigh*
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