1,2,3,4,5,6,7 are arranged such that sum of two successive numbers is a prime number. For example, 1234765 (i.e. 1+2=3, 2+3=5, 3+4=7....)
1. How many such possible combinations occur?
2. How many possible combination occurs if first number is 1/7 and last number is 7/1 (i.e 1xxxxx7 or 7xxxxx1)?
3. How many numbers will come on 4th position(xxx_xxx)? Choices.
A) How many such possible combinations occur?  B) How many possible combination occurs if first number is 1/7 and last number is 7/1 (i.e 1xxxxx7 or 7xxxxx1)?  C) How many numbers will come on 4th position(xxx_xxx)?  D) W3  E) 24
We have to follow a systematic approach for this question. We know that if at all two consecutive numbers be prime, they should not be even in the first place. So we arrange even numbers in even places, odd numbers in odd places.   2 should not have 7 as its neighbor   4 should not have 5 as its neighbor   6 should not have 3 as its neighbor   Case 1:   __ 2 ____ 4 ____ 6 __   x7 x7,5 x5,3 x3   So fix, 3 or 1 in between 2 and 4. We get the following options with reverse case also.   5234167, 7614325   5234761, 1674325   1234765, 5674321   3214765, 5674123   Case 2:   __ 2 ____ 6 ____ 4 __   x7 x7,3 x3,5 x5   5216743, 3476125   3256147, 7416523   3256741, 1476523   1256743, 3476521   Case 3:   __ 4 ____ 2 ____ 6 __   x5 x5,7 x7,3 x33412567, 7652143   7432165, 5612347   7432561, 1652347   1432567, 7652341   Answer 1: Total possibilities are 24.   Answer 2: 4 possibilities.   Answer 3: 3 possibilities.   Answer:How many possible combination occurs if first number is 1/7 and last number is 7/1 (i.e 1xxxxx7 or 7xxxxx1)?
<result>B</result>
1,2,3,4,5,6,7 are arranged such that sum of two successive numbers is a prime number. For example, 1234765 (i.e. 1+2=3, 2+3=5, 3+4=7....)
1. How many such possible combinations occur?
2. How many possible combination occurs if first number is 1/7 and last number is 7/1 (i.e 1xxxxx7 or 7xxxxx1)?
3. How many numbers will come on 4th position(xxx_xxx)?