Gold Coins, Bags, & Thieves

Sherlock Holmes and I were called to investigate the brutal clash between two gangs, taken place in a bar, a few nights ago. It was rumored that all ensued from burglary, for gold coins, to be exact. There were reports of burly men snatching numerous bags, each containing the same amount of gold coins, into their vehicle before they fled away in a hurry. Just a moment ago, Holmes returned with words from his informant, who had been spying at the thieves' whereabouts.

Holmes: My guy was there just in time to eavesdrop on the thieves' conversation outside as they were dividing the gold coins among themselves. Unfortunately, their voice was muffled, so the best clue he got was these three numbers, which I'm certain that they refer to the number of bags, the number of gold coins in each bag, and the number of thieves, of course. You can see that the difference of the highest and the lowest numbers is less than the lowest number itself.

The puzzle is that we don't know which number is for which, and there are 66 possible combinations of these mysterious numbers . Nonetheless, my guy took a look through a peephole and saw a remainder of 66 gold coins on the table after their division.

I: Well, with these numbers in our hands, can't we distinguish them by trying out all possible divisions?

Holmes: No, my friend, Watson. Even if we know all these numbers, we still can't rule out any combination.

What would be the least possible number of thieves in this incident?

Inspired by 3 Brothers Riddle


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