Problem Set #2- Math Question

Domo!

Last weeks Problem Set was quite hard, wasn't it?
But anyways, I chose question 8.
The question goes like this, "The average (mean) of a list of 10 numbers is 0. if 72 and -12 are added to the list, the new average will be...."

If you look at the question carefully it says a "list of 10 numbers is 0." What else gives you an average of 0? 0 of course!Now if you write down 10 zeros and add 72 on the right side and -12 on the other side, you will have 12 numbers. Now to find an average you add all the numbers and divide by the amount of numbers you have. -12+72= 60. Now, take 60 and divide by the amount of numbers you have. Which is 12! 60/12=5.

The final answer is 5. :D
My reflection on this is that it was easy since I have learned the basics. I think the key to solving these questions is being calm and adding up all the basics you've learned correctly and you will have the answer. Sometimes it may also require some guessing but that rarely occurs if you have your basics. I really like these problem solving Tuesdays. It gives me a break from doing repetitive stuff and gives me a challenge. Each question is different in its own way and it just feels refreshing and fun!

Feb 9, 2010 - Math Question

Domo!

So, for homework we had to do Math Problems. I did pretty well and our teacher told us to pick a favourite question. Okay! So the question I chose goes like this, "The greatest number of Mondays that can occur in the first 45 days of a year is..." So,this was really easy to explain.

First, you draw out a calendar. The question says "45 days" Then, you write out the numbers. From 1-45 because the question says so. So, you would write out "1" on the first Monday because you want the greatest number of Mondays. If you put it somewhere else, it will not work. Then you continue and eventually you will reach an end. After that, you count the number of Mondays that appear. You will get 7. Good Luck and try your best!

Tower of Hanoi

I must say, it was quite difficult!

My strategy was to watch the first couple seconds of the solution and then figure out the rest!

I've solved 4 disks and currently just solved 5 disks!

It is amusing yet difficult! (\#o_o)/

5 Disks:

The minimum moves for the 5 disks is 31. The first move you should do is move the smallest ring to far right. This is different from the 4 disks where you first move the smallest ring to the middle. I think for 6 disks you would move the smallest ring to the middle. So this suggests that when you have an odd number of rings, you would move the smallest ring to the far right. When you have an even number or rings, you would move the smallest ring to the middle.

Your objective would be to move the last ring to the right. In order to do that, you would have to move the rings above it away. What I found out is, when you move the rings properly they will always end up in the middle! Strange isn't it? Though the first moves are different, all the rings above the last ring will always end up in the middle. X_X

Once you move the last ring to the far right then your next objective would be to isolate the 4th ring. Another interesting thing I found out is when you have four rings in the middle and the last ring on the far right you would move the smallest ring to the empty left space. For the 4 disks, you would move the smallest ring with the last ring. This game is mostly about precision and if you make the right choices or if you make the unnecessary choices.

Formula. Okay. It is quite hard to figure out the formula but here we go.

No. of Disks No. of Moves

1 1

2 3

3 7
4 15
5 31

Observing the table, I've found out that all the minimum number of moves are all odds. This means it doesn't matter if you have an even number of disks because in the end you will have an odd number of moves. Here is a formula that will determine the number of moves. 2^n-1=No. of Moves. n will represent No. of Disks. Eg. 2^3-1=7, 2^4=16-1=15

It is a good formula ne?

Some good points when trying to solve the Tower of Hanoi

- First goal is to move the last ring to the right

-When you have moved the last ring to the right, check if your number of moves is half of the minimum moves required. This means that the next moves you make are heavy important. :D

-Let's say I'm trying to solve the 4 Disks and that I have successfully moved the last ring to the right. Half of the 15 would be 7. What I also found out was if you made the right choices then when you were half-way done it would be an odd number. It it was an even number half-way through or if the number of moves you have made was over half of the minimum moves required then restart. >.<

-Always move the smallest to a space available where it won't interfere with the movement of the other rings below it. This will be quite helpful.

Here is a picture of my personal experience with the dreadful 5 Disks!