MathDB

On a blackboard the product

log_{( )}[ ]\times\dots\times log_{( )}[ ]

is written (there are 50 logarithms in the product). Donald has

100

cards:

[2], [3],\dots, [51]

and

(52),\dots,(101)

. He is replacing each

()

with some card of form

(x)

and each

[]

with some card of form

[y]

. Find the difference between largest and smallest values Donald can achieve.

Problem Statement