MathLabs

Problem 4

Find all positive integers nn such that {n,n+1,n+2,n+3,n+4,n+5}\{n,n+1,n+2,n+3,n+4,n+5\} can be partitioned into two disjoint sets whose products are equal.
Step 3 of 4: Determine the only candidate
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In plain words

Once the smallest possible member is 11, the entire consecutive block is fixed.

{n,n+1,ldots,n+5}={1,2,3,4,5,6}\{n,n+1,\\ldots,n+5\}=\{1,2,3,4,5,6\}
Detailed analysis

Since the block contains 11, positivity and consecutiveness force n=1n=1. The candidate block is {1,2,3,4,5,6}\{1,2,3,4,5,6\}.