During the early ages, there was a flourishing city state. Let us call it Earlsdale.

Sagaris, the Treasurer of Earsdale had forgotten how many gold, silver and bronze coins were kept in the city vaults. So he decided to ask the three guards, each of whom guarded one type of coin, how many coins were in his charge.

However, the guards were uncooperative, and the best that Sagaris could get from each was a statement about the numbers of coins in the other two vaults.

• Dolius, who was guarding the gold, said there were 3000 silver and 5000 bronze coins.
• Termerus, who was in charge of the silver, said there were 3000 gold and 5000 bronze coins.
• Battus, who was protecting the bronze, said there were 4000 gold and 3000 silver coins.

Unfortunately, only one guard was completely truthful. Each of the other two guards stated at least one false amount.

If there were 12,000 coins altogether, how many of each type were there?

Visualize the data:
D:  ____  3000  5000
T:  3000  ____  5000
B:  4000  3000  ____

If Dolius is truthful, Gold must be 4000, but then Battus is also truthful.  Rejected.
If Termerus is truthful, Silver must be 4000,
     which is possible if Dolius is lying about Silver and Battus is telling 2 lies.
If Battus is truthful, Bronze must be 5000, but then Dolius is also truthful.  Rejected.

Gold: 3000
Silver: 4000
Bronze: 5000

Posted by Larry on 2023-04-20 09:08:54