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
The cost of Tesla shares are currently $600. If I buy 100 Tesla shares and then Tesla shoots up by 25% of it’s stock price, how much profit would I obtain?
Puzzled?
What is the total cost of all the shares after the stock shoots up?
Take the answer you got in the previous hint and subtract the amount that I initially paid for it!
Let’s say that I bought 1000 shares of Tesla this time at $600. Now, if I want to make a profit of $15,000 dollars, what would the share price of Tesla need to be?
Puzzled?
How much is my initial investment? My investment after the stock price changes needs to be $15,000 more than that amount.
Divided our desired total investment(after the price change) by the number of shares that we have to find the desired cost of Tesla shares.
ANSWERS TO LAST WEEK’S PUZZLERS
Last Week's Puzzler Quik
Careera From Nigeria was the winner of this shout-out!
The word “quick” has 5 different letters. When we rearrange it, we have 5 choices for the first letter, 4 for the second, and so on. Thus, our answer is $5\cdot4\cdot3\cdot2\cdot1=120$
Last Week's Puzzler Think
Srimanth from Illinois was the winner of this shout-out!
Since MISSISSIPPI has 11 letters, draw eleven lines and fill each in with the number of available letter choices, e.g. 11 options for the first, 10 for the second, and so on…
Since MISSISSIPPI has 11 letters, draw eleven lines and fill each in with the number of available letter choices, e.g. 11 options for the first, 10 for the second, and so on…
This is equal to 11! or 39,916,800 permutations.
But is this correct for the unique permutations of the letters in MISSISSIPPI?
Consider this…
What happens if I switch the 3rd and 4th letters in MISSISSIPPI and leave all else the same? Are those different permutations?
Nope.
The 3rd and 4th letters are both S’s so switching them changes nothing. The above calculation is an over count because of these repeat letters.
So how do we adjust for these extra repeated arrangements?
Adjusting for Repeats
To adjust our calculation we need to divide out the duplicate permutations. Finding them isn’t too difficult.
First determine what causes repeated arrangements. This comes from letters that occur more than once. For MISSISSIPPI that includes 2 P’s, 4 I’s, and 4 S’s.
Let’s start with the P’s. For every permutation, we can make an identical permutation with the P’s in opposite positions. So to adjust for these duplications, we must divide by 2! (the number of ways we can arrange the 2 P’s).
To adjust for the repeated I’s, divide by the number of ways we can arrange 4 I’s, which is 4!.
Lastly to account for the 4 S’s divide by another 4!.
Thus, we get $$\frac{11!}{2!4!4!}=34,650$$
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