Registration is now open for the next contest!
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
What is the Least Common Multiple of 12, 16, and 20?
Puzzled?
First, find the prime factorization of each number!
Compare the prime factorization of each number!
What is the greatest common factor of the first four powers of 2 and the first four powers of 3? Note that the first power is taking the number to the power of 1.
Puzzled?
Break this problem into steps!
Find the GCF of the powers of 2 and the powers of 3 seperately and then find their GCF!
ANSWERS TO LAST WEEK’S PUZZLERS
Last Week's Puzzler Quik
Felicity from Lander, Wyoming was the winner of this shout-out.
Let’s say we want to make a meal. We write each course in the 3 blanks ___ ___ __. We can have soup or juice, so there are 2 choices for how to fill the first blank: Soup ___ ____ or Juice ___ ___. Similarly, we have 3 choices for the main course, and 2 choices for dessert. Since each choice is independent from one another, we have a total of 2*3*2=12 different meals.
Last Week's Puzzler Think
This week’s shout out goes to Aidan from IL! Kudos to him!
We use standard combinatorics to get 4!. (4 * 3 * 2 * 1) for five different keys(we divide by 5 since the key chain can be rotated). However, the ability for the chain to flip halves the number of combinations (as both the regular and the flipped are considered to be the same), and brings us to our answer: $$\frac{4!}{2} = \frac{24}{2} = 12.$$
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