As always, no Algebra allowed (meaning no variables), use only arithmetic (numbers, multiplication, divison, etc.), logical reasoning and your imagination.
Long ago, when few people were versed in the art of counting, there was a great storm on the ocean. A ship, battered by the typhoon, was saved thanks to the exceptional work of two sailors.
When the storm was over, the captain, determined to reward his two captains for the well done service, announced that he would share the contents of a small chest of gold coins among them the next day, and charged his first mate with the task.
It turned out that the two sailors were very good friends, and wanting to avoid the embarrassment of a public sharing, one of them had the idea in the early hours of the morning to get his share of the prize. Going to the chest, this sailor separated the coins into two identical groups and, to his surprise, there was one coin left. Not knowing how to proceed, he threw it into the sea to thank the gods for his survival and then took his share.
Later, however, the second sailor had exactly the same idea. Going to the chest, he separated the coins into two equal groups and, to his surprise, there was one coin left. He threw it into the sea as a thank you for his luck and then took his share of the reward.
In the morning the two sailors felt embarrassed to report the night's procedure. So the first mate separated the coins into two groups and found that there was one left. He gave each sailor his share of the prize and took the remaining coin for himself as payment for his calculations.
Knowing that the ratio of coins won by the first and second sailors was 29/17, determine the minimum amount of coins that were originally in the chest.
Long ago, when few people were versed in the art of counting, there was a great storm on the ocean. A ship, battered by the typhoon, was saved thanks to the exceptional work of two sailors.
When the storm was over, the captain, determined to reward his two captains for the well done service, announced that he would share the contents of a small chest of gold coins among them the next day, and charged his first mate with the task.
It turned out that the two sailors were very good friends, and wanting to avoid the embarrassment of a public sharing, one of them had the idea in the early hours of the morning to get his share of the prize. Going to the chest, this sailor separated the coins into two identical groups and, to his surprise, there was one coin left. Not knowing how to proceed, he threw it into the sea to thank the gods for his survival and then took his share.
Later, however, the second sailor had exactly the same idea. Going to the chest, he separated the coins into two equal groups and, to his surprise, there was one coin left. He threw it into the sea as a thank you for his luck and then took his share of the reward.
In the morning the two sailors felt embarrassed to report the night's procedure. So the first mate separated the coins into two groups and found that there was one left. He gave each sailor his share of the prize and took the remaining coin for himself as payment for his calculations.
Knowing that the ratio of coins won by the first and second sailors was 29/17, determine the minimum amount of coins that were originally in the chest.
