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
A man has 53 socks in his drawer: 21 identical blue, 15 identical black and 17 identical red. The lights are out and he is completely in the dark. How many socks must he take out to be 100 percent certain that he has at least one pair of black socks?
Puzzler Think
Thanks to homeschoolmath.net, for this week’s Puzzler Think.
A teacher wrote a large number on the board and asked the students to tell about the divisors of the number one by one.
The 1st student said, “The number is divisible by 2.”
The 2nd student said, “The number is divisible by 3.”
The 3rd student said, “The number is divisible by 4.”
.
.
.
(and so on)
The 30th student said, “The number is divisible by 31.
The teacher then commented that exactly two students, who spoke consecutively, spoke wrongly.
What is the sum of the positions of the two students who spoke wrongly?
Want a hint? Contact me at aditya@thepuzzlr.com
Answers To Last Week’s Puzzlers
Click here to go to last week’s Puzzlers
Puzzler Quik
There are many tedious ways to do this problem involving casework. One such way is to count the # of times that Joseph decides to take 2 vitamins(i.e 1,2,3,4,5 days) and finding the total # of combinations for each. But the Puzzler aspires to bring you interesting puzzles that are not just boring computation, but rather have a concept behind it.
If you were able to find the concept for the Puzzler Quik this week, pat yourself on the back. The concept that can be applied to this problem is recursion. Let me explain further. If Joseph had only 3 vitamins, he could have either taken two vitamins or one vitamin on the last day. If he had taken two vitamins on the last day, then he has one vitamin left over. If he had taken one vitamin on the last day, then he has two vitamins left over. Therefore, the number of ways that 3 vitamins can be taken is equal to the number of ways that 1 vitamin can be taken(1 way) plus the number of ways that 2 vitamins can be taken(2 ways). We can generalize this for “n” number of vitamins.
Number of ways that “n” vitamins can be taken = Number of ways that “(n-1)” vitamins can be taken + Number of ways that “(n-2)” vitamins can be taken =
Since we already know how many ways we can take 1 or 2 vitamins, we can create a chart
| # of vitamins | Adding the last two terms | Total Number of Ways |
| 1 | Does not apply | 1 |
| 2 | Does not apply | 2 |
| 3 | 1+2 | 3 |
| 4 | 2+3 | 5 |
| 5 | 3+5 | 8 |
| 6 | 5+8 | 13 |
| 7 | 8+13 | 21 |
| 8 | 13+21 | 34 |
| 9 | 21+34 | 55 |
| 10 | 34+55 | Our answer- 89 |
We have now arrived at our answer, which is 89. The method of recursion we used for this problem is common to deducing the answer to a whole range of tough math problems. In fact, our argument can be used to prove the Fibonacci sequence.
Still have questions? Email me at aditya@thepuzzlr.com for a more in-depth explanation.
Puzzler Think
There are many fancy ways to do this problem, but the simplest way is the one below:
The deduction that needs to be made to make this problem a piece of cake is that the two numbers that multiply to 225 must BOTH be larger than the two numbers that multiply to 16. Let us make a chart to list out all the pairs of factors. Remember, the two factors must be different.
| First Factor of 16 | Second Factor of 16 | First Factor of 225 | Second Factor of 225 |
| 1 | 16 | 1 | 225 |
| 2 | 8 | 3 | 75 |
| 5 | 45 | ||
| 9 | 25 |
We can now note that we must minimize the larger factor of 16 and maximize the smaller factor of 225. Doing that, we get our wanted pairs:
2 * 8 = 16 and 9*25=225
So the numbers on the blackboard are 2,8,9, and 25. Since there is no other way to add another number on the blackboard without breaking at least one condition in the problem, we have our answer: The sum of the numbers on the blackboard is 44.
Have any questions? Want to send me a puzzle to possibly be the next puzzler? Email me at guptaa2.aditya@gmail.com