The Second ThePuzzlr contest is tomorrow!
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
Matt flips 
coins. Those that land heads, he sets aside. He then reflips the coins that landed tails, and again sets aside all those that land heads. Finally, he flips a third time the coins that landed tails twice, and again sets aside all those that land heads.
What is the expected number of coins Matt sets aside?
Puzzled?
Use Expected values
1/2 of the coins are expected to be heads each flip. Put those coins aside and repeat!
What is the sum of the solutions to the equation
$$ \sqrt[4]{x} = \frac{12}{7 – \sqrt[4]{x}}? $$
Puzzled?
Let $$y = \sqrt[4]{x}$$
You will get a quadratic for y which you can then use to find the sum of the possible values of x.
ANSWERS TO LAST WEEK’S PUZZLERS
Last Week's Puzzler Quik
Adriana from Texas was the winner of this shout-out.
We can set up an equation with the four people as A,B,C, and D. We have A+B+C+D=13. Now suppose that we have all the pancakes lined up in one line, and we have 3 barriers that separate the pancakes into 4 groups, the first one belonging to A, the second belonging to B, the third belonging to C, and the last group belonging to D. Since the barriers and pancakes are indistinguishable, and we have 16 total “items” (13 pancakes and 3 barriers) and we need to choose 3 barriers, there are 16c3 or 560 ways to distribute 13 pancakes to 4 people.
Last Week's Puzzler Think
This week’s shout out goes to Emmett from Lebanon, Ohio! Kudos to him!
We let the expression on the left hand side be x. Then, if we examine the expression inside the first square root, we find that it is equal to k+x. Next, we square both sides, which gives us k+x=49. Now, from the original equation, we find that x=7. Plugging this in gives us k=42.
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