The Baby and the Beast
26/06/2005 09:40 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
izmeinaAside from pottering online and slinking in Cyberia and reading the occasional book or two, the Izzie has found herself yet another ingenious form of procrastination.
Mean green thing that she is, the Izzie very rarely buys the newspapers but prefers to read them in cafes. After all, it is not the wood pulp and smudgy print that we are after but the content. And newspapers, no more than books that you own rather than get from libaries – the chances of reading them decreases dramatically when actually owning them as you can always get around to it later.
So our latest diversion is new on the puzzle pages, even though it has been apparently around in other parts of the world for ages. It's not like Izzie to follow a fad but this is a particular intriguing one.
First time Izzie seen one of these critters, thinks – that looks straightforward enough but we only have another 15 minutes at the cafe before having to catch the bus and go home to feed the monsters
The puzzle consists of a 9 by 9 grid of squares divided into smaller 3 by 3 grids. Thought at first it was some new incarnation of magic squares where each row and column and diagonal have to add up to the same number. It's a bit simpler but not necessarily easier. You only have to fill in the numbers from 1 to 9 so that each appears only once on each row and column and also in each of the 9 smaller grids. It's proper title is Sudoku but Izzie prefers to call it Rubik's cube for Flatlanders.
First time we tried it, used brute force. Went through every single empty cell and filled in with pencil all the numbers that could possibly fit and then after doing that for all of them, looked to see which ones were most likely. Problem was, it was way too easy to miss numbers that way and it was most tedious indeed. Next refinement was to list the unused numbers in each 3 by 3 grid and then test them out in the blank cells.
Finally got more into the big picture by looking at rows or columns of 3 grids and use the position of a number appearing twice to narrow down its location in the third grid.
This was infinitely more efficient. In some cases – what we call the Baby puzzles, not only would they give you lots of prefilled numbers – often as high as 40 filled squares out of the possible 81. But they would put them in the handiest places so that solving the puzzle became not much more than a case of filling in the blanks. Less than ten minutes would do it. Positively boring.
But then there was the Beast which appeared in Monday's paper. They gave us only 19 of the total 81 cells and all evilly and randomly shuffled so that the usual trick of searching for two of the same number in a row or column was not going to give away the location of the third. Well – certainly not directly.
(Izzie has forgotten how to do tables so will just use X where the blank spaces should be.)
X9X XXX XXX
XXX 36X X5X
XXX 2XX XXX
2X5 XXX 4XX
XX3 X8X 6XX
XX7 XXX 1X9
XXX XX1 XXX
X4X X79 XXX
XXX XXX X3X
Must have spent somewhere between 3 and four hours on this little bugger but never did solve it. It's not like Izzie to give up so easily but the best way out of a hole is to stop digging.
The good thing about these puzzles is that you don't have to wait until next day to check your answer because it either works or it doesn't. If you've got it right you will know.
In the end, Izzie peeked at the answer next day because it was obvious we had run into a very large brick wall. Turned out that we had the whole middle row of 27 cells perfect plus correctly deduced another ten cells but could just not use this information to get the rest. Most peeved indeed but we can always try another one tomorrow.
Another beast was amazingly like the rubik's cube. The Iz never did manage to solve that infernal cube. The nearest we got was 6 cells of the wrong colour scattered on the corners. Same thing happened with Wednesday's puzzle. Did not think it was possible to have only 7 cells wrong.
But all this weeping and wailing and gnashing of teeth finally paid dividends on Thursday when for the first time, we have finally solved a five star beast and did not take five hours to do it.
Seems silly to waste so much time on pointless puzzles but in some ways, they teach useful things that are hard to learn another way. Like these are solved using nothing but logic and deduction and the odd lucky guess. Each choice turns out to have ripple effects in far off corners that seem totally unrelated.
Another game Izzie used to play in her flobberworm days when we had time and lots of it was chess. Chess is an excellent way of learning how to see things from some one else's point of view and to develop long term thinking. But best of all, you pick up these things without even realizing it.
Also got to thinking how to go about working out the possible permutations and combinations. Like - the ways of arranging the numbers in any one grid would be 9x8x7x6x5x4x3x2x1 possible ways but not so sure about the whole collection in that once one grid is filled in, it automatically limits the possibilities for all the others. Of course - they are still pretty astronomical as for every possible correct way of filling the 81 squares, there is oodles of quizzes that can be made from it. (Wonders if just giving the centre number for each 3 by 3 box would be sufficient information to get the rest without taking ten centuries to solve it)
Mean green thing that she is, the Izzie very rarely buys the newspapers but prefers to read them in cafes. After all, it is not the wood pulp and smudgy print that we are after but the content. And newspapers, no more than books that you own rather than get from libaries – the chances of reading them decreases dramatically when actually owning them as you can always get around to it later.
So our latest diversion is new on the puzzle pages, even though it has been apparently around in other parts of the world for ages. It's not like Izzie to follow a fad but this is a particular intriguing one.
First time Izzie seen one of these critters, thinks – that looks straightforward enough but we only have another 15 minutes at the cafe before having to catch the bus and go home to feed the monsters
The puzzle consists of a 9 by 9 grid of squares divided into smaller 3 by 3 grids. Thought at first it was some new incarnation of magic squares where each row and column and diagonal have to add up to the same number. It's a bit simpler but not necessarily easier. You only have to fill in the numbers from 1 to 9 so that each appears only once on each row and column and also in each of the 9 smaller grids. It's proper title is Sudoku but Izzie prefers to call it Rubik's cube for Flatlanders.
First time we tried it, used brute force. Went through every single empty cell and filled in with pencil all the numbers that could possibly fit and then after doing that for all of them, looked to see which ones were most likely. Problem was, it was way too easy to miss numbers that way and it was most tedious indeed. Next refinement was to list the unused numbers in each 3 by 3 grid and then test them out in the blank cells.
Finally got more into the big picture by looking at rows or columns of 3 grids and use the position of a number appearing twice to narrow down its location in the third grid.
This was infinitely more efficient. In some cases – what we call the Baby puzzles, not only would they give you lots of prefilled numbers – often as high as 40 filled squares out of the possible 81. But they would put them in the handiest places so that solving the puzzle became not much more than a case of filling in the blanks. Less than ten minutes would do it. Positively boring.
But then there was the Beast which appeared in Monday's paper. They gave us only 19 of the total 81 cells and all evilly and randomly shuffled so that the usual trick of searching for two of the same number in a row or column was not going to give away the location of the third. Well – certainly not directly.
(Izzie has forgotten how to do tables so will just use X where the blank spaces should be.)
X9X XXX XXX
XXX 36X X5X
XXX 2XX XXX
2X5 XXX 4XX
XX3 X8X 6XX
XX7 XXX 1X9
XXX XX1 XXX
X4X X79 XXX
XXX XXX X3X
Must have spent somewhere between 3 and four hours on this little bugger but never did solve it. It's not like Izzie to give up so easily but the best way out of a hole is to stop digging.
The good thing about these puzzles is that you don't have to wait until next day to check your answer because it either works or it doesn't. If you've got it right you will know.
In the end, Izzie peeked at the answer next day because it was obvious we had run into a very large brick wall. Turned out that we had the whole middle row of 27 cells perfect plus correctly deduced another ten cells but could just not use this information to get the rest. Most peeved indeed but we can always try another one tomorrow.
Another beast was amazingly like the rubik's cube. The Iz never did manage to solve that infernal cube. The nearest we got was 6 cells of the wrong colour scattered on the corners. Same thing happened with Wednesday's puzzle. Did not think it was possible to have only 7 cells wrong.
But all this weeping and wailing and gnashing of teeth finally paid dividends on Thursday when for the first time, we have finally solved a five star beast and did not take five hours to do it.
Seems silly to waste so much time on pointless puzzles but in some ways, they teach useful things that are hard to learn another way. Like these are solved using nothing but logic and deduction and the odd lucky guess. Each choice turns out to have ripple effects in far off corners that seem totally unrelated.
Another game Izzie used to play in her flobberworm days when we had time and lots of it was chess. Chess is an excellent way of learning how to see things from some one else's point of view and to develop long term thinking. But best of all, you pick up these things without even realizing it.
Also got to thinking how to go about working out the possible permutations and combinations. Like - the ways of arranging the numbers in any one grid would be 9x8x7x6x5x4x3x2x1 possible ways but not so sure about the whole collection in that once one grid is filled in, it automatically limits the possibilities for all the others. Of course - they are still pretty astronomical as for every possible correct way of filling the 81 squares, there is oodles of quizzes that can be made from it. (Wonders if just giving the centre number for each 3 by 3 box would be sufficient information to get the rest without taking ten centuries to solve it)
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no subject
Date: 2005-06-27 01:24 pm (UTC)Oh, who am I kidding, we're going to Cornwall, it will rain!
Good luck with the puzzles.
nasty numberses
Date: 2005-06-27 01:57 pm (UTC)Would never dream of buying a book of them when that website seems to have a few online and just about every newspaper has one a day. Anyway -really should be doing something constructive like reading those library books due back on Thursday. But what we especially like about the little buggers - all you need is a pencil and a bit of time - no dictionaries or calculators or anything complicated.
Hope you don't get the weather you are expecting for your trip to Cornwall