PUZZLES
1) Here’s the scene. You and a math teacher face three wooden doors. Behind one is a valuable diamond bracelet. Behind the other doors are mud puddles. You don’t know what’s behind which door; the teacher does. You select a door, and the teacher – before opening the door you selected – opens another to reveal a puddle. The teacher offers you the opportunity to change your selection and win what lies behind the second unopened door, or stick to your first choice and win what lies behind that door. What should you do?
2) Every whole number can be obtained by multiplying a certain number of primes. For example, 48 requires 2×2x2×2x3, which is an odd number of primes. 49 requires 7×7, which is an even number. Every whole number is therefore odd or even in the number of primes required. By convention, 1 is considered even in this typology. As we rise through the whole numbers, do we encounter more even types, odd types, or are they equally balanced?
The answers to December’s puzzles were supplied in the December issue.
Here are the answers to this month’s puzzles:
1) The question is whether the odds are fifty-fifty that the bracelet lies behind one of the two unopened doors, and the answer is no. Work it through slowly. One time in three, the bracelet is behind the door you chose earlier. Two times in three, the bracelet lies behind the other unopened door.
2) The answer is peculiar. Except for #1, you find that you encounter either more odd types or an equal quantity of odd and even types. Until you reach 906,150,257. When for the first time you find that there have been more even types than odd. (We hope you didn’t test the numbers one by one.
