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.

Don’t forget to check out our new section: Mind Bogglers. It features counter-intuitive math thoughts and paradoxes.

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Are you interested in math and puzzles? Do you like winning money? Well, why not participate in ThePuzzlr Contest, a 40-minute, 30 questions test for all ages that will be available to take via our website! We even have a sample test to help you get a feel of the problems! If you have already signed up, be sure to share this with as many friends as you can.

Puzzler Quik

If $a=2,162$ , $b=7,389$ , and $c=25,412$ , find the remainder when the product $abc$ is divided by 10. Try not to just multiply out the numbers!

Puzzled?

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

Is it enough to multiply the last few digits of each number?

Hint 2:

You don’t need a second hint!

Puzzler Think

How many three-digit numbers satisfy the property that the middle digit is the average of the first and the last digits?

Puzzled?

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

Try casework!

Hint 2:

Let your cases be the possible value of the digit in the middle.

ANSWERS TO LAST WEEK’S PUZZLERS

Last Week's Puzzler Quik

Ishan from Ottawa Hills, Ohio was the winner of this shout-out. His explanation was superb!

Here is one way to solve the problem:

Let the first digit be $a$ and the second digit be $b$ . We then have $$7(a+b) = 10a+b$$. Simplifying, we get $$7a+7b=10a+b$$ This simplifies to $$2b=a$$. Since we want to minimize our number and both $a$ and $b$ must be positive( $b\neq{0}$ as that would mean that there is no valid solution to $$2b=a$$), we can let $$a=2, b=1$$. This gives us our answer: 21!

Last Week's Puzzler Think

Despite receiving many correct submissions, the best submission that we received was by Carter from San Diego, California! Kudos to him for solving this problem!

Here is his explanation(slightly edited by me):

There are 30 participants in the tennis tournament. For each match that is played, exactly one person is eliminated. Since we want only one winner, we must eliminate 29 of the 30 people. This means that 29 rounds must take place!

Puzzled? Suggestions? Future Puzzlers? Holler at aditya@thepuzzlr.com

The Puzzler – Week 8