Thursday, April 3, 2014

different digits in a digital clock

The other day I was in the bus and there was a digital 12-hour clock in the middle, it was 3:21. I noticed all of the digits were different, when it changed into 3:22 I wondered: how many times a day are the digits in this type of clock different?
It is a really simple calculation to do:
For hours with 1 digit in the hour space (1–9): there are 9 possible values for the hour. It has 2 spaces for the minutes; in the first one there are 6 possibilities (0-5) in which one is repeated in the hour space. Then, in the second space, there are 10 possibilities (0-9) that can occur, but 2 cannot be used because they are repeated in the other two numbers.
                So: 9*5*8 = 360
For hours with 2 digits in the hour space (10-12): 11 cannot be used. There are 2 possible hours (10 and 12) and in the first value of the minutes there are 2 values that cannot be used, and in the second minutes value there are 3 values that were used before.
                So: 2*4*7 = 56
360 +56 = 416 à every 12 hours
There are 2 12 hour periods every day, 2*416 = 832

There you go: a digital 12-hour clock has all different digits 832 times a day.

Thursday, March 27, 2014

Female and shiny starter pokemon

The other day I was playing pokemon and I remembered some time ago my brother had told me starter pokemon were much less likely to be female. This led me to think if the probability of getting a shiny starter pokemon was less than any other pokemon’s chance.
I went online and I found out that the probability of getting a shiny starter was the same as any other pokemon, 0.0122%. Also, the probability of getting a female starter is 12.5%; almost 1000 times more than getting any shiny.
After this, I wondered: what is the possibility of getting a female shiny starter? This is what I did:
0.0122% of the 12.5% of females are shiny: 0.0122%*12.5% 0.000122*0.125 = 0.00001525 = 0.001525%.

Therefore it would take me about 100000 tries to get a female starter, which is so much more comparing to the 10000 tries to get any shiny starter. 

Thursday, March 20, 2014

The order of operation is (morally) wrong

this video I found explains how ambiguity lead to BIDMAS or PEMDAS, but even though this is helpful it is turning us into robots that don't even enjoy mathematics but are only in search for the answer. Really interesting!

Thursday, March 13, 2014

Pi day!

In case you haven't noticed, tomorrow is Pi day! (3/14). To pay homage to pi, I found a very cool page that finds out in what position any string of numbers are. For example, my birth date (04/05/98) is in the position 500651. Try it out!
 http://www.angio.net/pi/

Thursday, March 6, 2014

Lord of the Rings calculations

I've been wondering for some time how much time does the Lord of the Rings’ plot lasts. I did some research and I was able to create a timeline for the most important events until the ring is destroyed. Now everything I need to do is make the sum! *SPOILER ALERT* This post spoils some of the main events in the Lord of the Rings plot.

September 22, 3001 - Bilbo leaves the Shire.
April 13, 3018 - Gandalf tells Frodo about the ring.
Sept 26, 3018 - The Hobbits leave the Shire.
Sept 29, 3018 – The hobbits encounter Aragorn in Bree.
October 6, 3018 – Frodo is pierced by the Morgul blade.
October 20, 3018 - The Hobbits and Aragorn arrive at Rivendell.
December 25, 3018 - The fellowship leave Rivendell.
Jan 13 – the company reaches Moria.
Jan 25 – Gandalf falls with the Balrog of Moria.
Feb 15 – the fellowship reaches Lorein.
Feb 26, 3019 – the fellowship is scattered.
Feb 29, 3019 – Merry and Pippin find Treebeard.
March 2, 3019 – Frodo and Sam get to the end of the dead marshals.
March 3 – the ents destroy isengard.
March 5 – Theoden and Gandalf reach Isengard.
March 12, 3019 – Gollum leads Frodo and Sam into Shelob’s lair.
March 25, 3019 - The ring is destroyed.

All of the months in the Shire calendar have 30 days. A Shire year is 12*30=360 days long

From September, 3018 to March, 3019 there are 6 months, that’s 6*30 days, or 180 days. There’s almost 6 exact months since the start of the journey until the destruction of the one ring (1 day less). It took exactly 179 days to destroy the ring, if we count since Frodo becomes aware of the situation he’s in we would need to add 13 days (to get to April 26) and 5 more months (5*30 = 150 days), so the total would end up being 179+163=342 days, almost a full year!

We can also see that Frodo took (163/342)*100= 48% of the total time waiting on Gandalf, forcing the Fellowship to have their adventure starting in the winter.

I kept doing some calculations just out of curiosity, kind of finding out what characters are more productive and to give some use to the other dates in the timeline (none of them count the waiting time at the start):
Time spent in Rivendell: 2 months (60 days) + 5 days = 65 days, that is (65/179)*100 = 36% of the journey
Since Merry and Pippin were separated from the fellowship it took them 5 days (to get to march 1) + 2 days = 7 days to destroy Isengard with the aid of the Ents. That’s (7/179)*100 = 4% of the journey! (This didn’t delay the ring’s destruction though)

It took Frodo and Sam 1 month (30 days) – 1 day =29 days to destroy the ring. That is (29/179)*100 = 16% of the time

The first time of the journey (until the fellowship was scattered, without counting the waiting time) took 5 months (150 days), (150/179)*100= 84% of the journey, while the second part (from the scatter of the fellowship to the destruction of the ring) took 29 days, (29/179)*100 = 16% of the journey. I consider this break of first and second part of the journey fair because the distances are similar (the first part is a bit longer) and I also considered that Frodo and Sam had no horse/pony and had to choose another way into Mordor after finding the first one. Just in case I chose other frontiers:

From the leaving of the Shire until their arrival at Rivendell; then to the destruction of the ring (keep in mind Rivendell is SO much closer to the Shire than to Mordor): first =30-6 = 24 days, (24/179)*100 = 13%. Second: 5 (to get to oct 25) + 5*30 = 155 days, (155/179)*100 = 87%

From the leaving of the shire to the leaving of the fellowship from Rivendell; then to the destruction of the ring: first: first = 3*30 (3 months)-1 day = 89 days, (89/179)*100 = 50%. Second: 3*30 = 90 days, (90/179)*100 = 50% (Yay! I found where they were at the middle of the time by accident!)

Form the leaving of the Shire until the arrival at Moria; then to the destruction of the ring: first = 17 (to get to oct 13) +3*30= 107 days, (107/179)*100= 60%. Second= 12 (to get to jan 25) + 2*30 days = 72 days, (42/179)*100= 40%

From the leaving of the Shire until they arrive at Lorein; then to the destruction of the ring: first = 19(to get to oct 15) + 4*30 = 139 days, (120/179)*100 = 78%. Second= 10 days (to get to feb 25) + 30 days= 40 days, 22%

I don’t consider Rivendell a proper distance half since it is too far away from Mordor. My conclusion is: the first part of the journey took longer than the second part.


Note: I only used the calculator to get the percentages and the large sums; some of my steps in getting the answer were to make my like easier and less confusing. I added a map to help in guidance and orientation.






Thursday, February 27, 2014

The Beauty of Pi

Maths is a beautiful thing, but between operations that beauty is lost. It would be so much more fun for students that are struggling with this subject if they did something artistic once in a while, just to relieve the stress. I found this video some time ago that caught my attention explaining pi's beauty in the best way I could've thought. Enjoy!