Question 509194
<pre>
That's impossible because any two pages that face each other in a book
always consist of an even numbered page on the left and an odd-numbered page on
the right. So 288 can't possibly be the sum of their page numbers because the
sum of an odd number and an even number is ALWAYS an odd number, never an even
number.  Yet 288 is an even number.  So this cannot be.  Your teacher will have
to agree.

If the sum were 287 instead of 288, the problem would be possible. We would let

n = the page number of the page on the left 

and let

n + 1 = the page number of the facing page on the right.

then the equation would be 

n + (n + 1) = 289

  n + n + 1 = 288

     2n + 1 = 288
     
         2n = 288

          n = 144

So the number of the page on the left is n=144 and the 
page number on the right is n+1=144+1=145.

If you try that with the sum of 288, you get the
ridiculous answer that the page on the left is 
numbered {{{143&1/2}}} and the one facing it is
numbered {{{144&1/2}}}.  No book has pages 
numbered with fractions!

Edwin</pre>