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Home » Thus, the largest possible value of \(\gcd(a, b)\) is \(\boxed289\). - Imagemakers

Thus, the largest possible value of \(\gcd(a, b)\) is \(\boxed289\). - Imagemakers

📅 May 2, 2026 👤 scraface

May 02, 2026

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After adding 18, in sorted order, the value between 15 and 16 must be...
The values in (15,16) must have been in original set? Could be.
But in the new list, the three values that come after 15 are likely be...
Without exact data, but in olympiad context, assume minimal inference:...
Since 18 >16, and new median is 16, values <16 are those less than 16.
To get a5 + a6 = 32, need values >15 in position.
Only way is if the added value pushes the middle up, but 18 is large.
Perhaps original has values above 16.
The a5 in a 9-list needs to be at least 16 to have average 16 with a6.
Since sum a5+a6=32, minimum a5 is 16 (if a6=16).

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