Riddles
-
- Chronically Blathering
- Posts: 1522
- Location: Gainesville, Florida
Re: Riddles
A man takes turns, first drawing a horizontal line and then drawing a vertical line on a sheet of paper and then back to horizontal. It takes him 4 lines to draw one rectangle. If he continues this pattern(one vertical line after every horizontal line), how many vertical lines does it take him to draw 1 million rectangles, assuming he's using only one side of a single flat sheet of paper?
- gamecreator
- Prattles on Unremittingly
- Posts: 3116
- Location: Ukraine
Re: Riddles
1001? (1 plus square root of 1 million)
-
- Chronically Blathering
- Posts: 1522
- Location: Gainesville, Florida
Re: Riddles
nope, I assure you it's considerably less.
- Patdragon
- Game Master
- Posts: 2288
- Location: Isle of Wight
Re: Riddles
that would assume all the rectangles are the same size...(i think), I think ive heard this one before and its something like 31 but i can't remember how it was done exactly.
► Show Spoiler
- Karn, Silver golem
-
- Chronically Blathering
- Posts: 1522
- Location: Gainesville, Florida
Re: Riddles
That's closer, but still definitely off. And you're on the right track, Patdragon.
- gamecreator
- Prattles on Unremittingly
- Posts: 3116
- Location: Ukraine
Re: Riddles
Oh, you mean not only the smallest ones, but rectangles composed of other rectangles.
Then It is not possible to get exactly 1 million, but after 46 vertical lines he would have 1071225 rectangles.
Then It is not possible to get exactly 1 million, but after 46 vertical lines he would have 1071225 rectangles.
-
- Chronically Blathering
- Posts: 1522
- Location: Gainesville, Florida
Re: Riddles
But are you sure that's the least number?
- gamecreator
- Prattles on Unremittingly
- Posts: 3116
- Location: Ukraine
Re: Riddles
After drawing 45 lines he would have only 980100 rectangles, so yes.
-
- Chronically Blathering
- Posts: 1522
- Location: Gainesville, Florida
Re: Riddles
Try thinking again. You are missing something.
- Patdragon
- Game Master
- Posts: 2288
- Location: Isle of Wight
Re: Riddles
half that then- 23 as you only need vertical lines?
► Show Spoiler
- Karn, Silver golem
-
- Chronically Blathering
- Posts: 1522
- Location: Gainesville, Florida
Re: Riddles
No, he's missing something, but it will probably go to him. He's calculating using vertical lines. But, by doing so, he's missing half the puzzle.
- Patdragon
- Game Master
- Posts: 2288
- Location: Isle of Wight
Re: Riddles
fair noth i'm stumped on it. tho my riddle mind says if he doesn't take his pen off the paper he does it in 4 or 5 (first line he draws after first 4) as he could draw one continuous line making rectangles
Last edited by Patdragon on Tue Apr 01, 2014 4:01 am, edited 2 times in total.
► Show Spoiler
- Karn, Silver golem
-
- Chronically Blathering
- Posts: 1522
- Location: Gainesville, Florida
Re: Riddles
Horizontal lines first, vertical lines last. It takes 91 lines to achieve 1 million rectangles. Thus, he completes the million with a horizontal line. The first part of the puzzle involves squares of triangular numbers. The second involves what happens by adding a single line. Anyways, giving it to gamecreator.
Last edited by Davecom3 on Tue Apr 01, 2014 4:05 am, edited 1 time in total.
- gamecreator
- Prattles on Unremittingly
- Posts: 3116
- Location: Ukraine
Re: Riddles
The text is ambiguous. I thought the step is finished only after a vertical line is drawn. But there is nothing in the text, that supports or contradicts this. So the man would have to draw 46 horizontal and 45 vertical lines. He would get 1024650 rectangles (however, still not exactly the million).
-
- Chronically Blathering
- Posts: 1522
- Location: Gainesville, Florida
Re: Riddles
If he's drawn 1,024,650 rectangles, he's also drawn 1 million rectangles. This is like how all months have 28 days. If he's drawn 1 million rectangles, having completed these with a horizontal line, even if afterwards he draws a vertical line, he didn't need to draw that vertical line to achieve that last bit of the million. But, in any case, your turn.