Change the order of numbers on a clock−dial so that sum of any two numbers of consecutive positions may be prime.


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Question Number 3146 by Rasheed Soomro last updated on 06/Dec/15

$C h a n g e t h e o r d e r o f n u m b e r s o n a c l o c k - d i a l s o t h a t$ $s u m o f a n y t w o n u m b e r s o f c o n s e c u t i v e p o s i t i o n s m a y$ $b e p r i m e .$
	Answered by prakash jain last updated on 06/Dec/15

	$1 \to 2, 4, 6, 12$ $2 \to 1, 3, 5, 11$ $3 \to 2, 4, 8, 10$ $4 \to 1, 3, 7, 9$ $5 \to 2, 6, 8, 12$ $6 \to 1, 5, 7, 11$ $7 \to 4, 6, 10, 12$ $8 \to 3, 5, 9, 11$ $9 \to 2, 4$ $10 \to 3, 7, 9$ $11 \to 2, 6, 8, 12$ $12 \to 1, 5, 7, 11$ $9 10 3 2 1 4 7 6 5 12 11 8$ $9 \to 19 17$ $10 \to 19 13$ $3 \to 11 5$ $2 \to 5 3$ $1 \to 3 5$ $4 \to 5 11$ $7 \to 11 13$ $6 \to 13 11$ $5 \to 11 17$ $12 \to 17 23$ $11 \to 23 19$ $8 \to 19 17$
	Commented by prakash jain last updated on 06/Dec/15

	$Thanks . Corrected .$
	Commented by RasheedAhmad last updated on 06/Dec/15

	$V V N i c e!$ $I n 3^{r d} l i n e I t h i n k^{'} 1^{'} s e e m s$ $m i s t a k e n l y$ $i n c l u d e d .$ $3 \to \underline{1}, 2, 4, 8; 3 + 1 = 4 \in P$
	Commented by RasheedAhmad last updated on 06/Dec/15

	$H o w m a n y s o l u t i o n s m a y b e ?$
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