Exploring Huan’s Birthday Puzzle: A Mathematical Journey

Imagine a scenario where a person, Huan, is celebrating his birthday and his age is a square number. Last year, his age was a multiple of 12, and next year, he will be a multiple of 10. What could be Huan's age?

The Possibilities

Let's explore the possibilities based on Huan's unique characteristics. Huan could be human, a Galapagos tortoise, a bristlecone pine, a volcano sponge, or even an alien from the planet Methuselah. Let's see which of these could fit the given conditions.

Huan as a Human

Since Huan is human, his age must be a square number. Let's see if we can find a suitable age:

16 (42) 25 (52) 36 (62) 49 (72) 64 (82) 81 (92) 100 (102)

Among these, we need to find an age that was a multiple of 12 last year and will be a multiple of 10 next year.

A Step-by-Step Solution

Let's go through the solution step-by-step:

Find the appropriate square number: The square numbers are 16, 25, 36, 49, 64, 81, and 100. Since next year his age will be a multiple of 10, let's look for a number whose last digit is 9 (since adding one to a multiple of 10 will result in a number ending in 9). Select the number: The only square number ending in 9 is 49 (72). So, Huan is 49 years old this year. Verify the conditions: Last year, Huan was 48, which is a multiple of 12 (12 x 4 48). Next year, Huan will be 50, which is a multiple of 10 (10 x 5 50).

Conclusion

Therefore, Huan is 49 years old. Last year he was 48, which is a multiple of 12, and next year he will be 50, which is a multiple of 10. This solution is clear and simple, avoiding complex algebraic calculations.

Quick Summary:

Huan is 49 years old, a square number of 7. Last year, he was 48, which is a multiple of 12. Next year, he will be 50, which is a multiple of 10.

Additional Tips

If you're working through similar puzzles, here are some quick tips:

Identify the square numbers within the given constraints. Check the last digit of the number to ensure it meets the next year's condition. Verify the previous year's condition.

With a bit of practice, you can solve these puzzles quickly without needing to write anything down.