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 prime numbers are their from 1 to 100.
Puzzled?
Pull out a table and go through the numbers.
It is not that hard! Just cross out the all the even numbers(except 2), since they are all multiples of 2. Keep on doing that for 3, 5, and so on.
What is the smallest positive integer that leaves a remainder of 1 when divided by 2, remainder of 2 when divided by 3, a remainder of 3 when divided by 4, and so on up to a remainder of 9 when divided by 10?
Puzzled?
Say if your number is “N”. What numbers is N+1 divisible by?
N+1 is divisibly by 1 through 10. Therefore, one possible value is the LCM of 1-10.
ANSWERS TO LAST WEEK’S PUZZLERS
Last Week's Puzzler Quik
Sam from Georgia was the winner of this shout-out!
Every pair of factors multiple to 12. The factor pairs of 12 are 1,12–2,6 –3,4. Thus, we get 12^3=1728.
Last Week's Puzzler Think
The shoutout for this problem goes to Elena from Florida!
Here is a video https://youtu.be/Z5UZCj3J2rU that comprehensively explains how to tackle these type of problems! Using the approach in the video, we find the prime factorization of 81. $$81=3^4$$ Thus, adding one to the exponent, we get that 81 has 5 positive factors!
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