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 number do you obtain when you multiply all the numbers on a calculator?
Puzzled?
What are all the numbers on a calculator?
You don’t need a second hint!
Can you Simply this: $$\sqrt{i}$$
Puzzled?
Let your answer be of the form a+bi
When you square a+bi, set the real parts equal to each other and the imaginary parts equal to each other.
ANSWERS TO LAST WEEK’S PUZZLERS
Last Week's Puzzler Quik
Alex from Oregon was the winner of this shout-out.
The observation we need to make is that if there are x lily pads one day, there will be 2x lily pads the next day! Thus, if it takes 48 days to cover a lily pad, it will take us 47 days to cover half of that, which is what we desire. Thus, our answer is 47 days!
Last Week's Puzzler Think
This week’s shout out goes to Abhinav from Sunnyvale, California! Kudos to him for solving the problem!
What we notice is that the exponent is so huge, so there is no way that we have to calculate this by hand, there is probably a pattern!
In fact, we notice that
i^1=i
i^2=-1
i^3=-i
i^4=1
i^5=i
i^6=-1
i^7=-i
i^8=1
…
Aha! We see a pattern! We notice the powers repeat mod 4. We also know that 640 is 0 mod 4. Therefore, the answer is i^4=1.
Pingback: The Puzzler – Week 31 -