Number Theory

 

In how many ways can the numbers 1, 2, 3, 4, 5, 6 be arranged in a row,    

so that the product of any two adjacent numbers is at least 5?    

 

You must have the 1 between the 5 and the 6.   

The rest of the numbers can be anywhere.   

 

So, consider two cases:   

 

(1) Permutation of   2  3  4  (5 1 6) ..... ₄P₄  =  24   

(2) Permutation of   2  3  4  (6 1 5) ..... ₄P₄  =  24   

 

Add them together                 total  .....  48 ways   

_.