One more cyclic number-16 digits

I had mentioned about cyclic number 142857 in my first blog.
Here is another example-a 16 digit number,starting (curiously you may think) with zero.
This number is the result of finding the reciprocal of 17,in which these16 digits occur in repetition,and obviously you can see that the first digit has to be zero.
The number is 05882352 94117647.
Let me give you a list of multiplicants which when used in multiplying this number give you new numbers where only the last righthandside digit moves to the front ,the remaining digits appearing in the same order in betwen.
Multiplication by 12.(M/12) gives                 70588235 29411764
M/8 -Multiplication by 8-gives you               47058823 52941176
M/11 gives you............................................64705882 35294117
M/13...........................................................76470588 23529411
M/3.............................................................17647058 82352941
M/2.............................................................11764705.88235294
M/7.............................................................41176470 58823529
M/16...........................................................94117647 05882352
M/5.............................................................29411764 70588235
M/9.............................................................52941176 47058823
M/6.............................................................35294117 64705882
M/4.............................................................23529411 76470588
M/14...........................................................82352941 17647058
M/15...........................................................88235294 11764705
M/10...........................................................58823529 41176470
You can see all the 16 multiplicants appear in the above list though not in the correct numerical order
You must be wondering what happens when you multiply with 17.You will get all sixteen of the digits as 9...........

Magic Squares

You must have heard about magic squares-viz squares with 3/3 cells or 4/4 cells filled with numbers when the sum of the numbers in each row/column/both diagonals are the same.However let  me now present some data.
I will deal with a 3/3 cell first.
The simplest is formed with the numbers from 1 to 9 .It will be like this-
4          9           2
3          5           7
8          1           6
The totals as per each row,column and both diagonals will be 15-viz .
3 times the number 5 in the central cell.
It is formed as follows-First put the number 5 in the central cell.Put the number 1 in the cell below it.Put the number 2 at the top row right hand corner.The numbers 1,5 and 2 will thus appear as in a clock showing the time as 06-07 or 06-08.Th rest of the numbers can be filled up to make the totals 15 everywhere.
You will be surprised to know that the squares of the numbers in each row viz those of 492,357 and 816 will add up to 1035369 while you will get the same total using the squares of the numbers formed in the reverse order viz 294,753 and618.Similarly the squares of the numbers in each column viz 438,951 and 276 will add up to 1172471 while you will get the same total using the numbers read upside down viz 834,159 and 672.
You can make squares with any number like 45 placed in  the central cell instead of 5 and using numbers like 37,39,41,43,47,49,51 and 53 instead of the numbers 1,2,3,4,6,7,8 and 9.The totals everywhere will be 135.
You can also have magic squares using prime numbers-sample shown below-
67         1         43
13         37       61
31         73        7-  the totals everywhere will be 117 .  

Trick with numbers on strips

Here is a game or trick you can play with your friends/relatives
You need 5 cardboard strips of equal length.Each strip is to be neatly divided into 6 parts.
First part you could name them as A,B,C,D and E,this title appearing at the top of each of these strips.
The remaining parts will carry numbers as shown below-
A         B          C         D         E
8         8           7          3          9
4         3           6          9          7
5         6           1          9          7
7         9           5          8          5
8         7           9          7          6

You can show the strips to your friends/relatives and ask them to place them in any order they like side by side  for example ABCDE,...CEADB or BEACD.
In every case you will be able to tell immediately the total of the 5 numbers appearing in the group of strips
For ABCDE it will be 356194....For CEADB it will be 317593 and for BEACD it will be 367516.
The trick is based on the digits written at the 4th part in each strip namely 5,6,1,9 and 7.The totals in each strip in the remaining parts have been kept at 27.So the totals of the 4 numbers in those strips will be 29997 or 30000 minus 3.So for ABCDE the totals for all the 5 strips will be 30000+56197-3=356194.
Similarly for the arrangement CEADB it will be 30000+17596-3=317593..and for BEACD it will be 30000+67519-3=367516 as mentioned above.
You  can easily tell the total in any other arrangement.In fact 120 arrangements are possible.
You can have even 6 or 7 strips so that  6 digit numbers or 7 digit numbers will be available.
You can even place digits at  another part on each strip like the 3rd part or 5th part instead of the 4th.
You can also make the totals of the digits in remaining parts as 36 instead of 27.In this case you need to add 40000 and deduct 4 to the number appearing on the special part viz the 4th chosen by you.
You can choose the digits in  the other parts in whatever way you like so that the totals are27.

Words to numbers-Black hole number 4

In my blog under Nadamadumnumbers I had mentioned about Number 123 being a Blackhole number.
Here is another example of a Blackhole number.
Take any whole number and write out it's numeral in English such as FIVE for the number 5.Count the number of characters in this spelling.In this case it is 4 or FOUR.So work now with 4 or FOUR.You will get 4 again.
Another Example 152.This appears as ONE HUNDRED FIFTY-TWO.Now count the characters.You may include spaces and hyphens in your count.The total count is 21.Repeat again with 21 i.e TWENTY ONE.This gives the count 10.viz TEN.Repeat again with TEN.You get 3 or THREE.Repeat again 5 or FIVE.Repeat again You will end up with 4..Similarly 163 will gradually  give you 23,12,6,3,5 and finally 4.
Try with any other number.You will always end up with 4,the blackhole number.
Do you not find this interesting?
Though the result is language dependent,other languages may have a comparable property but not necessarily with 4 as the Blackhole.

Table Calendar-2012

A few days ahead to welcome the New year and time for making a search for new calendars.
I thought I can show a way of making a table calendar for one's own house/room.
Months in each year can be classified into 7categories depending on the weekday pertaining to the first day of the month..The categories can be named after alphabets like A,B,C,D,E,F,and G..If you are of religious mind you can use K,R,I,S,H,N and A.Alternative notations HOCKEY,GWALIOR,PTNEHRU etc.
Let me use the notation KRISHNA....K stands for the month in which the first day is Sunday,R stands for the month in which it is Monday etcetc.The calendar for 2012 can be notified by KSHKINKSARHA.
The calendar will look like this-
                                 K            R         I           S           H          N        A
1   8   15   22   29   Sun.        Mon     Tues      Wed     Thurs     Fri      Sat  
2   9   16   23   30   Mon        Tues     Wed      Thurs     Fri       Sat      Sun
3   10  17  24   31   Tues        Wed   Thurs       Fri         Sat      Sun      Mon
4   11  18  25    -     Wed       Thurs    Fri         Sat         Sun     Mon    Tues
5   12  19  26    -    Thurs        Fri       Sat         Sun        Mon   Tues    Wed
6   13  20  27   -     Fri            Sat      Sun         Mon      Tues   Wed    Thurs
7   14  21  28   -     Sat           Sun     Mon        Tues      Wed   Thurs    Fri
You can use a different colour pen or pencil  for each category like K or R so that reading the same will be easier.You can also prepare cardboard slips -6 will be necessary  -to block out the columns which do not relate to each month.
In fact you can prepare similar calendars for many more years to come adopting the following notations-
2013-INNRSARHKINK
2014-SAAIHKINRSAR
2015-HKKSNRSAIHKI
2016-NRINKSNRHAIH
2017-KSSARHAINKSN
2018-RHHKINKSARHA
2019-Same as for 2013
2020-SAKSNRSAIHKI
I hope the calendar will not be difficult to make or to read it when it is made.           

Before I continue to my next I would like all to see my second blog under the link.http://nadamadumnumbers.blogspot.com
Now for continuation let me introduce 3 numbers which show some fun.They are  explained below-
312132-This is of 6 digits containing the digits 1 to3 each appearing twice.There is one digit between the two ones,2 digits between the two 2's and 3 digits between the two 3's.
41312432-similar fun with two more digits ,a pair of 4's added.You can see 4 digits between the two 4's
17126425374635-Similar fun with a pair of 5's, a pair of 6's and a pair of 7s. 

Cyclic numbers

Let me start with the famous cyclic number 142857.
This is the period in the reciprocal of the prime number 7.viz when you attempt finding the reciprocal these 6 numbers get repeated.
When you start multiplying this number with 3,you get 428571,i.e the digit 1 at the left end moving to the right the other digits remaining undisturbed.When you now multiply the number with 2 you get 285714 the digit 2 also similarly moving.Similar multiplications with 6,4 and 5 you get  857142,571428 and 714285 again with similar continuous movements.More funny details in my next post.