Solution for the Problem of the Week #2

Posted: September 30, 2013

Since Juan's number is a multiple of 5, his number can be 5, 10, or 15. However, clue 2 says that Maria's number is more than Juan's number and clue 3 says Anna's number is exactly two times Maria's number. Thus if Juan's number were 10 or 15, Maria's number would be greater than 10, and Anna's number would be greater than 20. Hence Juan's number has to be 5. Since clue 4 says that Carlos' number is 1/3 Anna's number, the greatest possible value for Carlos' number is 6; otherwise, Anna's number would be over 20. But clue 4 also says that Carlos' number is not the smallest number, so we know it cannot be less than 5, because Juan's number is 5. Hence, Carlos' number has to be 6, and Anna's number is 18. Lastly, Maria's number is half of Anna's number, which is half of 18, or 9. Therefore Juan's number is 5, Maria's number is 9, Anna's number is 18, and Carlos' number is 6. There was no winner for this week's problem.