Question 27
Lucía writes the integer numbers from $1$ to $27$, in some order, around a circumference. Then, she calculates the sum of each pair of adjacent numbers, thus obtaining $27$ sums. We call $A$ the largest of these sums and $B$ the smallest. Find the minimum possible value of $A - B$.
Show how Lucía can write the numbers to obtain that minimum value and explain why it is not possible to obtain a smaller value.
Show how Lucía can write the numbers to obtain that minimum value and explain why it is not possible to obtain a smaller value.