## Monthly Archives: October 2017

### The infinite hotel paradox : due Jeff Dekofsky

This hardcore stuff about “infinity” , quite nicely, explained was pointed out to me by my ISC XII student, Mr. Utkarsh Malhotra! 🙂

### Permutations and Combinations: IITJEE Mains problem solving practice

Problem 1:

Find all natural numbers n such that $n!$ ends with exactly 26 zeros.

Problem 2:

Find the largest two digit prime that divides $200 \choose 100$.

Problem 3:

Find all natural numbers $n \leq 14$ such that $n! + (n+1)!+(n+2)!$ is divisible by 25.

Problem 4:

When $30!$ is computed, it ends in 7 zeros. Find the digit that immediately precedes these zeros.

Problem 5:

Prove that $\frac{(n^{2})!}{((n)!)^{n+1}}$ is a natural number for all $n \in N$.

Cheers,

Nalin Pihwa.

### A test about tests!

“We had to answer all the questions, just “Yes” or “No”.” Fran explained. “The first paper I got only five wrong.”

Ben smiled. “That sounds good. What about the other paper?”

“Tough, but the same number of questions,” the girl replied. “I got just a third of them wrong, so over all I got 75 percent right for the two papers.”

How many questions in each paper?

Cheers,

Nalin Pithwa.

### Daddy knows best!

“It’s only teenage infatuation,” Tom declared. “I do like Bob, but he is double your age.”

“Come on, Dad, that’s nothing these days,” Cathy replied. “He doesn’t look it, and anyway three years ago the digits of my age added up to the same as the digits of his age did.”

What they call a non-sequitur? How old was she?

Reference: Entertaining Mathematical Teasers, and how to solve them by J.A.H. Hunter, Dover Publications Inc., New York, available at Amazon India.

Cheers,

Nalin Pithwa.