## Archive for March 15, 2021

### Happy as L!

On Wednesday, I’ll complete my 50th trip around the Sun. To celebrate, my friend Kris sent me a card with a wonderful Roman reminder of my age:

Thanks, Kris!

Here are two relatively easy math problems associated with my birthday:

- On Wednesday, how many days old will I be?
- What are the four positive integer factors of the answer you got to Question 1? (Hint: One of the factors is the number of
**weeks**old that I’ll be.)

I recently wrote a book called One Hundred Problems Involving the Number 100. To celebrate my 50th birthday, here are ten problems involving the number 50:

- There are 50 puppies to be adopted at a shelter, and 98% of them are hounds. How many hounds must be adopted so that 90% of the remaining puppies are hounds?
- Let A = 1, B = 2, …, Z = 26. Find two common English words for which the product of the letters is 50.
- What’s the least possible product of two prime numbers with a sum of 50?
- While finding the sum of the numbers 1‑10, I got distracted and omitted some numbers. The sum of the remaining numbers was 50. How many different sets of numbers could I have omitted?
- The square numbers are 1, 4, 9, 16, …, and the non-square numbers are 2, 3, 5, 6, 7, 8, 10, 11, and so on. What is the 50th non-square number?
- Choose three numbers so that one number is selected in each row and each column. What’s the sum of the three numbers?

- A two-player game is played on this number rack with five rows of 10 beads. One player chooses to be Odd, the other Even. The players take turns. On each turn, a player may slide one, two, or three beads from the middle to the side of the rack. Beads moved to the side cannot be moved again. When all beads have been moved, the Odd player earns one point for each row with an odd number of beads on each side, and the Even player earns one point for each row with an even number of beads on each side. The player with the most points wins. What is the optimal strategy, and who should win?
- How many people must be present to have a probability of 50% that two of them will share a birthday?
- Insert only addition and subtraction symbols to make the following equation true:

9 8 7 6 5 4 3 2 1 = 50

- What’s the area of the square? (Inspiration from Catriona Agg, both for the puzzle and for the reduction in words.)

Answers will be posted on my birthday — St. Patrick’s Day! Stop back on Wednesday!