Wow, it is hard to believe that the school year is almost over! This will be the final installment for the Math POTW for this current school year. Thank you to all who provided answers, added to discussions, asked clarifying question, etc.
A BIG special thanks to those Bugtas kids, who answered nearly EVERY Math POTW over the course of the year. Not only did they always provide full details, but they helped keep ME up-to-date and ensured that I had weekly questions posted.
Below is the final Math POTW. Please answer in as much detail as you can. Also, comment on others too!
Below is the final Math POTW. Please answer in as much detail as you can. Also, comment on others too!
If you have 6 black socks, 4 blue socks, 8 brown socks, and 2 red
socks in your sock drawer, what is the minimum number of socks that you
need to pull out in the dark to be sure you had a matching pair?
I think that the minimum amount of socks you need to pull out are 5. This is because there are a total of 4 different coloured socks, so even if when you pick out 4 socks, and they're all miraculously different colours (because the probability of ACTUALLY getting all 4 different colours are pretty low), the fifth sock you choose will for sure make a pair.
ReplyDeleteHaha, I know I missed out on a few POTW's this year, but it was really fun, and I'll miss it *tear tear ;__;. Hope we can continue this next year!!!!!
I hope that we can continue the POTW next year too!
DeleteGreat work on this question Emily. I think you got to end on the high note that you wanted!
What might be a way that we could visually represent your thinking?
Hi. My sister and I did this together
ReplyDeleteWe think that the answer is 5
This is how we got this answer.
We assumed that "minimum" meant as something that is not realistic and more theoretical. This means that in identifying the number of socks needed to be pulled, we did not consider the mathematical aspects of this question (percentage, probability).
Instead, we said for every one sock (black,blue,brown,red) there are 3 other possible outcomes (3 other colors based on initial grab)
e.g
Black - Blue, Brown, red
Brown - Black, Blue, red
Simply put, for every one color, comes 3 different colors. This means that there has to be a minimum of 4 pulls to create such a result.
Since the question asks for a matching pair, there must be 5 pulls. 5 pulls means that the one extra pull will be either of the four colors that have been already pulled (assuming that 4 colors appear in 4 pulls).
e.g
Black, Blue, Brown, Red (have been pulled - 4 pulls)
+ 1
= Black,Black,Blue,Brown,Red
:o No way. It worked...theoretically. Hehehe
Goodbye. Have a good year. Cheers
- Jon and Rach
:'-)
Another great detailed response from you two. I like how you made somewhat of an equation to help explain your thinking.
DeleteThanks for the many great responses to the POTW this year. Stay tuned (Rachel) for future POTWs!