#### There are two numbers whose product added to the sum of their squares is 109, and the difference of whose squares is 24. What are the two numbers?

**Answer: ** 5 and 7.
(5)² = 25(7)² = 49(5x7)+25+49=10949-25=24

**Solution: **

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#### There are three guards and three prisoners who need to cross a river. Their boat only holds two people at a time, and the number of prisoners must NEVER be allowed to outnumber the number of guards on either side of the river; otherwise, the prisoners will overpower the guards and, well, the story will come to an abrupt end. List each of the trips that need to be made and who is in the boat, and who is on each of the riverbanks during each trip. How many trips it will take to safely transport all of the guards and prisoners across the river?

**Answer: ** The riddle "GUARDS AND PRISONERS" is unanswered. Do you know the answer? If so, click ANSWER and add your answer in the comments section.

**Solution: **

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