I spend the last two days learning about permutation and combination, all to solve a grade 7 ICAS maths question.
The fact that I only studied maths till grade 10 and that too in Malayalam has made it very difficult for me to remember much of what I studied. So I had to buy a grade 10 text book and go through it again.
The question that I was trying to solve was
The bank machine has four rows of buttons
1 2 3
4 5 6
7 8 9
0
Sam has a 4 digit bank number that uses one button from each row. For eg his bank number could be 0571.
How many different possibilities for Sam’s number are there.
Initially I thought there could be 3 choice from row 1, 3 from row 2 so on so forth.
And i got the answer 27. That made no sense. There had to be more than 27 combination of numbers, or anyone could hack the ATM pin code. (I know I don’t think like most and have a weird sense of logic)
This morning I finally figured , perhaps I need to look at the numbers 0471,0852, and 0963
That would give 24 ( 4 digit number 4 X 3 X 2 X 1) combination of each number. So 72 combinations.
Am I right?
Update: I just looked at the numbers again and I miseed so many numbers…for eg 0753, 0752, 08630841 etc etc.
So there has to be an eqation. What am I missing?
Now this brings me to my heartache for the day.
I, as an adult couldn’t solve a question like this, why would I want to make my child even attempt this question? Why would I frustrate them when they don’t get the answer?
Then again I firmly believe practice makes perfect.
I know Senna ( I am forever in love with him) wouldn’t have been 3 time champion if he hadn’t worked hard to get it ( That reminds me, it is 16 years this month)
Do I get my children to practice all these questions, so they can do the test well? What would they gain if they get High distinction? Where do i draw the line?
May be this site will help you with permutation and combination…
http://www.mathsisfun.com/combinatorics/combinations-permutations.html
sorry, can't help you with the other q 😀
exclude 0 for the time being
u can make 3 x 3x 3 = 27 numbers if the position of the rows are fixed. (as in first digit is from 1st row, 2nd digit of pin from 2nd row and so on)
from each of these 27 numbers u can make 6 different numbers by changing the position i.e 27x 6 = 162
in in each of these numbers u have 4 positions to add a 0
27x 6 x 4 = 648
Hi Sarah,
I think you should make them attempt this question because you are giving them a chance to find out what they are good at. If they find it interesting, there is a wonderful world of mathematics awaiting them .. And if they dont get the answer .. you can help them understand that there is no need to get frustrated. You can help them realize the fact that they dont have to be perfect in everything they do, its okay to let go and continue with their interests..
May be i am too young and inexperienced to say this ..but this is what i feel from a student's perspective .. 🙂
btw .. i am a regular reader of your blog for a really long time .. but never really got down to commenting … kudos to you for being what you are right now .. all the best 🙂
–meenu
I still remember the day I heard about his death. Summer vacation had begun; I was at a friend's, and she had a cable connection and it was all over star TV! Its so weird, how I was upset abt feeling upset over someone I know only through sportstar pages or occasional cable TV; how I had a small fight because I wanted to hear the news over and over again and she wanted to change to Zee coz she was into cricket and didn't care for Formula one!
Hi,
I am a regular reader here..Thought will let you my thoughts.. From the first three rows, you can select a number each..So, total ways = 3C1 * 3C1 * 3C1 = 27. There are 4 numbers in the pin, these can be arranged in 4! ways. 4! = 24. So the total number of ways = 3C1 * 3C1 * 3C1 * 4! = 27 * 24 = 648.
I am not sure abt the correctness, have been out of touch for a while.
As for your kids, I think it helps them realize if they are passionate about Maths. I used to love Maths as a kid and used to get kick from doing complicated questions (especially in an exam). Also, I think from a brain perspective, you are actively making more neuron connections, so it will help them for a while. Again, its such a layman's way of telling medical science. I am sure you being doctor will know all the science behind it. Also, you are teaching them to try hard. Thats a lesson you should be very proud of teaching your kids.
Cheers!
Ann