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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:

  1. The first and second numbers are prime.
  2. The third number is a multiple of the second number.
  3. The second number is even.
  4. The third number is more than nine and less than twenty.
  5. The first number is less than ten.
  6. The fourth number is the least common multiple of the first two numbers.
  7. The fourth number is the largest of all four numbers.
  8. The first number is more than three times the second number.
  9. 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?