"Where the mind is without fear and the head is held high;
Where knowledge is free;
Where the world has not been broken up into fragments by narrow domestic walls;
Where words come from the depth of truth;
Where tireless striving stretches its arms toward perfection;
Where the clear stream of reason has not lost its way into the dreary desert sand of dead habit;
Into that heaven of freedom it should be our intent.
( my adaption from Rabindranath Tagores famous lines)

Monday, December 29, 2008

Escott sliding Block Puzzle

Apart from the "Rush-Hour" type of puzzles there is the conventional one. One of the most exciting ones is the one invented by E.B.Escott, an American Mathematician in 1938. Martin Gardner said of this puzzle that "It is the most difficult sliding block puzzle "that he has seen. The optimum solution will be 48 moves counting each movement of one block as a single move even if it goes around a corner if the space is empty.

This is how I finished with Juan. NIM is one of my favorite games and it really tests the mind, there are various “modes” of it which you can play on my site shown in LINKS on RHS referred to as “My Mindgames”. Here I show you in my voice video of what is the most well known BASIC NIM consisting of 3 piles. Turn your volume on and listen to the way to play and solve it which is the best way to solve using the binary code.

If you have trouble in conversion go to the ready chart

This puzzle was invented by a French Mathematician Edouard Lucas in 1883. The problem is to transfer the tower of ‘n’ disks from that peg to any of the other 2 vacant pegs, moving one disk to a time and never placing the a disk on top of a smaller one. This is to be accomplished in the least number of moves.

The puzzle is also referred to as the “Tower of Brahma” situated in the holy city of Benares, India. Legend has it that there were 64 disks of Gold on one “peg” and that the priests are engaged in transferring the disks and when the last move is made the world will end . The formula for the least no. of moves is 2 raised to the power of ‘n’ minus 1. Assuming that there is no wrong move and if it takes one second per move, it will take 15 secs to transfer 4 disks and just about 4 minutes for 8 disks and about one month for 15 disks…. But roughly 600 billion years for all 64disks.

To play this game there are several sites but I recommend this link as the best:

http://www.mazeworks.com/hanoi/index.htm

I suggest you see the solutions below before attempting to solve the puzzle. That it.

There are several types of sliding puzzles that stimulate the human mind apart from being fun to solve.Here I am demonstrating a RUSHHOUR puzzle designed by Noki Yosgihara.RUSHHOUR sliding block puzzle invented by Nob Yoshigahara in the late 1970s The goal is to get THE RED car out of a n-by-m grid full of automobiles by moving the other vehicles out of its way. However, the cars and trucks (set up before play ) obstruct the path and are so intertwined that a typical puzzle requires many moves to complete.

Below...I have also given a solution to the puzzle using SBPsolver , a freeware utility created by Soft Qui Peut.

AND....... if you like to tackle such "RushHour Puzzles" goto the site mentioned below where you will find a lot of them to play AND get their solution. You can also create them on line www dot puzzleworld.org/SlidingBlockPuzzles/rushhour.htm

This is an ancient Chinese Shapes Game where the puzzle is posed as an integrated image and one has to solve the puzzle with all the pieces of different shapes given. This is very much like a jigsaw puzzle except that it always has the same pieces and all of the same color. In other words the picture puzzles themselves have been made by fitting together all the pieces in several different ways. Standardization is that the BASIC STRUCTURE is a square cut into seven pieces as shown here. These are 2 identical large triangles, one medium sized, another 2 identical smaller triangle, a square and a parallelogram. The 2-D picture-puzzles are usually of humans, animals and birds (many in motion) and other common objects like houses, boats, constructions and sometimes plain geometric shapes. The basic STRUCTURE is shown in Fig.A.

Two examples of a puzzle and their solutions are shown here. They are taken from the bird series and marked as Puzzle A and Puzzle B. These Tangram puzzles have engaged the attentions of mathematician like author Lewis Carroll, and puzzle makers Henry Dudeney and Sam Loyd. No wonder the game in Chinese is called "Seven-Board Game of Cunning". It has also been claimed that the famous theorem of Pythagoras was solved by the Chinese using this basis.The animations shown here is a result of the puzzles taken from a book by Joost Elffers called "Tangram" and published by Penguin Books which has over 500 puzzles with their solutions. (Fig B)

However I having played with this game many times I wish to make a color animation to promote this hobby.

There are several types of puzzles that stimulate the human mind apart from being fun to solve. The most famous and commercially successful sliding block puzzle was invented in the 1870's. It was known as the “15 puzzle" or BOSS puzzle. The puzzle consists of a block of 15 numbered small square blocks within a larger square box (4 x 4) capable of holding 16 such blocks, with one empty space. These are set at random (by sliding) to get an arrangement and the player has to slide them (without lifting) to get them in order with the last space vacant as shown in FIG 1.

One of America's greatest puzzle expert, Sam Loyd,"drove the entire world crazy" (as he himself put it) with this newly invented puzzle. (Now it has been discovered that he did NOT invent this puzzle but falsely took credit for it.) He had made it famous by offering a prize of $1000 for a correct solution of the puzzle. As Martin Gardner puts it "'Thousands of people swore they had solved it but no one could recall the moves and collect the prize.Loyd's offer was safe because this particular one was not solvable.".

Of more than 20 trillion possible arrangements of the squares, exactly half can be made by sliding the squares if the initial position is as shown in FIG 1 and thereafter jumbled up randomly. But if the 14 and 15 are interchanged and then jumbled up, we have a disturbed the ‘parity’ (to use the language of permutational mathematics)". And is not solvable. I now show you a video of how to solve it using an algorithm used by 'THEmuteKi' in Youtube.