| Show PO POPULAR AB rU PUZZLE E I Favorite Among Young Apprentices In Sixteenth and Seventeenth Centuries Con Cen How tunes How t tt-J tt Ja Solved It has been suggested that the grasshopper grasshopper grasshopper grass grass- hopper was a great favorite among the young apprentices of be the city cUy of or London in the sixteenth and seventeenth centuries Readers will have the he curious brass grasshopper grasshopper grass ss grasshopper hopper on the Royal exchange This loved long c escaped the fires of ot 1666 and 1 litt P The grasshopper after his his his' kind was the crest of Sir Thomas Gresham merchant grocer who died in 1579 and from this cause it has bas been used as a sign by grocers in gener general 1 Unfortunately for tor the legend as to ltd its origin the puzzle was only produced so late as the year 1900 On twelve or thirteen black disks are placed numb numbered ed counters Sr fir grass grass' grasshoppers hoppers The puzzle la is to make I l to 6 change places with those numbered 7 to 12 12 the vacant disk being left Inthe in inthe inthe the same position a as at present Move one at a time in any Cider ceder either to the adjoining vacant disk or by JumpIng JumpIng Jump Jump- Ing over one grasshopper like the rove in draughts Nos 7 to 12 can only move In the direction of ofa a clock hand and the others the opposite way Note also I that 1 and 6 j jS S 8 2 11 1 12 Grasshopper Puzzle 12 must to re left next to the vacant disk and try to find the tha fewest possible possible pos pos- possible sible moves The fewest possible moves in which this puzzle can be solved are 62 Here Is one way of doing it Of Ot course the numbers are those of the counters count ers and as there can never be more than one vacant disk each play whether it be a single move or a leap explains Itself 12 1 I 2 12 12 11 10 I 1 1 2 2 3 4 12 11 11 10 9 8 I t 2 3 4 5 5 12 11 10 y 1 8 7 12 6 1 I 2 2 3 3 4 5 6 1 I 11 10 9 9 8 7 12 2 2 3 4 5 6 6 6 I 1 10 10 9 9 8 7 7 12 4 4 5 6 1 1 8 7 12 6 1 I 12 Whatever may be the number of grasshoppers going each way the square of this number added to four Cour times that number added J to 2 will always always al ways be the number of ot moves re re- required Thus In the above case 36 plus 24 plus plus plus' 2 equals 62 I |
