Welcome to The Puzzler. Every week, there are 2 new puzzles related to my passion: math, logic, and thinking. The first puzzle will be The Puzzler Quik, meant for those who crave something fun-sized. The second puzzle will be The Puzzler Think, meant for those who love to ponder. The answers will be posted in next week’s column. Don’t forget to submit your answer for a potential shout-out in the next edition of the Puzzler.

Puzzler Quik

How many permutations of 3 digits are there, chosen from the ten digits 0 to 9 inclusive?

Puzzled?

Here is a hint to help you get going in the right direction:

How many choices do we have for each digit?

Hint 2:

If you can arrange something in “a” ways and something else in “b” ways, the total # of ways to arrange them is “a” times “b”.

Puzzler ThinK

In how many ways can we pick 3 balls out of 8 distinct pool balls

Puzzled?

Here is a hint to help you get going in the right direction:

(HINT: ORDER DOES NOT MATTER)

Hint 2:

Try seeing how many choices do you have for the first ball, second ball, and third ball. Divide by 6 to account for the fact that order does not matter(why?).

ANSWERS TO LAST WEEK’S PUZZLERS

Last Week's Puzzler Quik

Arvind from California was the winner of this shout-out!

We can rewrite 20! as 20 times 19!. Then, we have $$\frac{20\cdot19!}{19!}=20.$$ Thus, our final answer is 20.

Last Week's Puzzler Think

The shoutout for this problem goes to Alex from Ilinois!

Zeroes are made every time there is a factor of 2 and 5(why?). There are more factors of 2 then 5 so it suffices that we count the number of factors of 5 in 1000!. We can do this by following this process:

Take the number that you’ve been given the factorial of.
Divide by 5; if you get a decimal, truncate to a whole number.
Divide by 5² = 25; if you get a decimal, truncate to a whole number.
Divide by 5³ = 125; if you get a decimal, truncate to a whole number.
Continue with ever-higher powers of 5, until your division results in a number less than 1. Once the division is less than 1, stop.
Sum all the whole numbers you got in your divisions. This is the number of trailing zeroes.

Doing this for 1000!, we get 200 + 40 + 8 + 1 = 249 trailing zeroes!

The Puzzler – Week 39