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
In how many ways can you distribute 13 pancakes to 4 people?
Puzzled?
Maybe set up some equation with the number of pancakes given to each person as the variables?
Search up distributions!
Can you find the value of k?
$$\sqrt{k+\sqrt{k+\sqrt{k+\sqrt{…}}}}=7$$
Puzzled?
Use substitution!
Set the LHS = x and then substitute!
ANSWERS TO LAST WEEK’S PUZZLERS
Last Week's Puzzler Quik
Alex from Illinois was the winner of this shout-out.
Since this is a cubic equation, we can turn into this form: (x – a)(x – b)(x – c) = 0, where a, b, and c are roots. The only combination that work under the restrictions of sum of 7 and a product of 12 is 2,2, and 3. Therefore, there are only 2 distinct roots to the equation.
Last Week's Puzzler Think
This week’s shout out goes to Pranav from Pennsylvania! Kudos to him!
By Vieta’s Formulas, the sum of the roots of the quadratic equation ax^2 + bx + c, where a, b, and c are constants, is
-b/a. In this scenario, a = 1, b = -3, and c = -1, so -b/a = -(-3)/1 = 3/1 = 3.
You can also solve this using the quadratic formula, where the roots are (-b+-sqrt(b^2 – 4ac))/2a. Substituting in the values of a, b, and c, the roots are (3+-sqrt(13))/2, so the sum is (3 + sqrt(13) + 3 – sqrt(13))/2, and because the sqrt(13)s cancel out, this is equivalent to (3+3)/2 = 6/2 = 3.
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