Sunday, 29 September 2013

A Day for every Date- beat the calendar!

            One of the most impressive feats of mental calculation: calculate the day of any random date in your head. While it may sound extremely tough, if you are friendly enough with numbers, we reckon you can calculate days within 10 seconds! YES! All you need to do is remember some numbers and tricks and you will be ready.

Each day of the week is assigned a number-

This list is pretty easy to remember and follows a standard chronological order. NOTE that the numbers are 'wrapped' around the number 7; this modulo behavior is extremely important for this trick to work.

Next, we give each month a number. Now, this list doesnt follow a logical order and we recommend that you develop your own method to remember this list-

January-6 (5 for leap years)
February-2 (1 for leap years)

            Once you have learnt these month codes, you can progress to the all important year codes. Just like months, every year has its own code but remembering year codes is an ordeal in itself and nearly impossible (unless you have an eidetic memory!). Fortunately, there is an efficient way to calculate year codes mentally. We shall demonstrate the method below-
We want to figure out the year code for 2005. Now, 2005 lies in the 21st century and ends with the number 5. We divide 5 with 4 and calculate the quotient (ignore the remainder), which in this case is 1. Then we add the obtained quotient to the last digit. 5+1 = 6. 6 is the year code for 2005. 
Lets find the year code for 2014. 2014 ends with 14. When we divide 14 with 4, the quotient is 3. Adding 3 and 14 we get 17. Next, we find which multiple of 7 that is smaller than 17 is closest to 17. In this case the multiple is 14. Subtract 14 from 17 to get 3; the year code for 2014

            The above method works for only 21st century years, for 20th century years, we have to add 1 to the final code.
1996- 1996 lies in the 20th century and ends with 96. The quotient when we divide 96 and 4 is 24. Add 24 and 96 to obtain 120. The closest multiple of 7 smaller than 120 is 119. 120-199=1. 1 is not the year code. We need to add 1 because 1996 lies in the 20th century. 1+1+2. So, the year code for 1996 is 2, and not 1.

Just like for 20th century years, we add 1; for 19th century years we add 3 and for 18th century years we add 5. The good thing about our calendars is that years are repeated after 400 years, so 18th century and 22nd century calendars are the same.

NOTE- Year codes will always lie between 0 and 6.

            Once you have mastered the trick for calculating year codes, you can proceed to the final step, calculating the day! We shall work out two examples-

1) 2nd March 1997:
   The month code is 2
   Calculate the year code- you will obtain 3
   The date- 2
Now add the three numbers, you will get 7. Now, 7 is our day code which represents Sunday. So, 2nd March 1997 was a Sunday

2) 22nd July 2222:
   The month code is 5
   Calculate the year code- you will obtain 2 (simply obtain the year code for 1822)
   The date-22
Now add the three numbers, you will get 29. Now, 29 is greater than 7 and needs to be reduced. We will now subtract the multiple of 7 closest to 29 but smaller than it from 29, which in this case is 28. 29-28=1. 1 is the day code for Monday. So, 22nd July 2222 will be a Monday.

We hope that you have now gained a clear idea of how to calculate days. If you need any assistance feel free to contact us via our blog.

Monday, 2 September 2013

The 3 Kid Problem

The main problem discussed in The Mathematics Symposium-2 was 'The 3 kid problem', the video for which can be found in the link below:

The 3 Kid Problem

Before you guys start scratching your heads and delve into this problem, there are some things that we want you to take care of, things that will come in your mind while watching the video:

1) The number mentioned on the 'board' is not shown to you for a reason, the main trick of this problem lies in decoding the 'mysterious' number
2) We mention in the end that the eldest kid plays soccer, please don't make any relations between the sport and the child's age. For all we care, he might have been a badminton player; the sport has NO relation with the child's age.

We will soon be posting the solution video!!