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Riddle Of The Frog's Ring

One Christmas the Abbot offered a prize of a large black jack mounted in silver, to be engraved with the name of the monk who should put forth the best new riddle. 
This tournament of wit was won by Brother Benedict, who, curiously enough, never before or after gave out anything that did not excite the ridicule of his brethren. 
It was called the "Frogs' Ring."

A ring was made with chalk on the floor of the hall, and divided into thirteen compartments, in which twelve discs of wood (called "frogs") were placed in the order shown in our illustration, one place being left vacant. 

The numbers 1 to 6 were painted white and the numbers 7 to 12 black. 
The puzzle was to get all the white numbers where the black ones were, and vice versa
The white frogs move round in one direction, and the black ones the opposite way. 
They may move in any order one step at a time, or jumping over one of the opposite colour to the place beyond, just as we play draughts to-day. 
The only other condition is that when all the frogs have changed sides, the 1 must be where the 12 now is and the 12 in the place now occupied by 1. 
The puzzle was to perform the feat in as few moves as possible. 

How many moves are necessary?

I will conclude in the words of the old writer: 
"These be some of the riddles which the monks of Riddlewell did set forth and expound each to the others in the merry days of the good Abbot David."

See answer



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