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Question 1. Can any 3-digit prime be transformed into any other 3-digit number following the Doublet rule?

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Question 2. What is the longest distance i. For the first question the answer is yes , for the second question the answer is 6 ,. To solve the question i used both Java and Wolfram , the idea is this i made a graph with nodes being the primes with 3-digits and there is a line between two nodes iff the primes representing the nodes are 1-Doublet meaning with one digit change we can transfer one into another and then we can state you question as graph theory question which are :.

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Playing Doublets with the Primes Ask Question. One could ask the same questions about 4-digit primes. Ahmad Ahmad 2, 1 1 gold badge 7 7 silver badges 25 25 bronze badges. A template-based implementation of generic graph search plus detailed explanation can be found on-line , which serves as the basis for the code used in this article and should therefore be thoroughly studied first.

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The famous 8-queen puzzle asks the player to find ways to put eight queen pieces on a chess board such that no queen piece can attack any other ones. In other words, no two queen pieces can be put on the same row, the same column, or the same diagnal.

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This puzzle can be readily solved with a tree-based search, which is a special case of graph search. There is a package of the name atscntrb-bucsgraphsearch for generic graph search that is stored on-line , and the content of the package is available for viewing here. One can simply use the npm tool for node package management to install the package directly by issuing the following command-line: npm install atscntrb-bucsgraphsearch. The following lines in QueenPuzzle.

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The odd "1" goes face down to the table and must not yet be identified. Bidding Each player has three bid-cards, one of each suit. Having examined your hand, decide which will be your bug suit, and select the card of that suit from your bid-cards. When everyone is ready, you all flip your bid-cards over and leave them face up so everyone knows everyone else's bug suit. At this point, two additional bids are possible, namely: Turnip.

This is a bid to accept as your bug suit that of the undealt card, whatever it may be, for the advantage of a doubled score.

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Indicate this by announcing "turnip" and leaving your bid-cards face down. Doublets , or "Double or quits".

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This amounts to a guarantee that you won't take any cards of your bug suit in tricks. If successful, you will score double.