If Only Kris Could Remember the Combination...
Kris found a treasure box. To open the box, she had to put four numbers in their correct order, using the following clues:
- The first and second numbers are prime.
- The third number is a multiple of the second number.
- The second number is even.
- The third number is more than nine and less than twenty.
- The first number is less than ten.
- The fourth number is the least common multiple of the first two numbers.
- The fourth number is the largest of all four numbers.
- The first number is more than three times the second number.
- The third number is one more than the sum of the first two numbers.
She opened the box and found a treasure equal to 1000 times the sum of the four numbers. How much was the treasure worth?
Source: Oregon Mathematics Teacher, Sept. 2000, p. 43
Hint: You do not have to use the clues in the order given. In fact, the latter clues are sometimes the most valuable.
Solution Commentary: According to the Source, the numbers are 7, 2, 10, and 14...making the treasure worth $33,000.
Do you agree with their answer?
Also, were all of the clues necessary?
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