Rensselaer Republican, Volume 12, Number 26, Rensselaer, Jasper County, 12 March 1880 — An Alleged Solution of the Puzzle of Fifteen. [ARTICLE]

An Alleged Solution of the Puzzle of Fifteen.

It ia possible that the pnblieatkm of a solution of the famous puzzle of fifteen blocks may interrupt rudely the reveries of the philosophers who have either solved the problem for themselves or have the leisure to toil over its intricacies. But the conviction that a solution will bear an olive branch of peace to countless stricken households prompts the writer of this article in a spirit of broad philanthropy to offer what appears to be one of several keys to the game. For the sake of clearness lat us ftnrt agree that the row of numbers next to the side of the box furthest from the holder, and containing the numbers 1, 2, 3 and 4, shall be called A. The next parallel row, containing the numbers 5, 6, 7 an 4 &r be called B; and the third row. containing the numbers 9, 10, 11 and 12, be called C. We shall see that B and C are the important rows in our solution. At the outset, instead of getting the lower numbers in their numerical order the quicker way to a solution is to arrange eleven numbers in their proper order on the outside rows of the box. That order, it will be seen, is 1,2, 3,4, 8, 12, 15, 14, IS, 9,5, and we can begin with any one of these numbers and .qvork either one way or both ways. This order can be quickly secured by using the four central squares and three blocks. Move into the central square the outer block (any one of those numbered above), turn it until opposite its E roper place and make a vacancy for it y removing a block from another part of the outer rows and shifting the outer blocks around. So easily is this done that we leave it to the ingenuity of our readers without further instructions. Tho outer blocks having been arranged the puzzle is limited to the four central squares and the numbers 6, 7. 10, 11, which will rarely come in their proper order. These four numbers are susceptible of twenty-four combinations, which, however, as we shall show hereafter, may be resolved into two, namely, a double inversion (in row B 7, 6 and in row (J 11. 10) and a single inversion (row B correct and 11, 10 in row C). The double inversion is solved as follows, understanding the mandatory word move before each of the numbers which follow: 12, 8,6, 10, 11, 7, 10, 6,8, 11, 6. 10, 7,6, 10, 7,6, 10, 11, 12. Let the foregoing formula be called X. The single inversion (row U correct and 11, 10 in row C), which seems to involve the whole secret of the puzzle, will be solved by moving the following numbers in the order prescribed: * 12, 8, 7 10, 11, 6, 10, 7,-8, 11, 7, 10, 6, 7,1 LB, 10, 11,. 7,6, 11, 10, 8,7, 10, 11, 6, 10, 7, 8. 11, 7, 10, 6,7, 11, 8, 12. We have now 7, 11 in row B and 6, 10 in , row C. Move all the outer blocks until number 5 is shifted four places and is next to 6. Move the box one-quarter around and it will be seen that the solution is complete. Let the foregoing formula be called Y. •

We have now disposed of three of the twenty-four combinations possible with the four central numbers. The three are: (1) The right order, (2) one Rouble inversion and (8) one single inversion. Any one of the remaining -twenty-one combinations can be quickly converted into one of the foregoing three by applying to them repeatedly the method of moves in formula X or the method represented in the first eight moves of formula X, or both methods combined. The moves are to be tho same, though the order of numbers will of course be different. Formula X and also its first eight moves should therefore be practiced carefully before any conversion of the twenty-one combinations is tried. After the double or single inversion is obtained they can then be solved by formulas X and Y respectively. All this, which appears complex and difficult on paper, will be readily understood when the box can be used for illustration. The time for solving the puzzle from the beginning is fpom four to ten minutes. Any possible combination of the number! can, in the way we have explained, be merged into some one of the combinations of the four central blocks, and then solved by the formulas given. This applies, of oourse. to the final combinations of 15, 14, 13, and 13, 15, 14, ant} 14, 13, 15, which have been so trying to the nerves and tempers of our provincial friends in Rochester.--N. Y. Post. ,