Parentheses can be inserted into the expression
1/2/3/4/5/6/7/8/9/10/11
to produce a large collection of numbers, some of which are integers. What is the quotient of the largest of these integers divided by the smallest?
I considered parentheses between /2, /3, /4, ......., /9, /10 and /11
Of the nine cases,
The minimum was 77, obtained by: 1/2/3/4/5/(6/7/8/9/10/11)
The maximum was 9979200, obtained by: 1/(2/3/4/5/6/7/8/9/10/11)
and, no! There was no case involving "parentheses within parentheses" that went below the minimum value or exceeded the maximum value.
Thus, overall we have:
Maximum value = 9979200, and
Minimum value = 77
Therefore, the required quotient = 9979200/77 = 129600
Puzzle Solution
