Right and left

The number 21978 is formed out of the 5 digits 2,1,9,7 and 8
If the digits are taken from right to left ,the number formed will be 87912
You will find that 87912 is four times 21978.
Such numbers are not definitely very easy to find. 

Reverse a magic square-Corrigendum

There was a small mistake in my previous blog-The actual position is as follows-
There are 3 magic squares,formed with the numbers 11,16,18,19,61,66,68,69,81,86,88,89
91,96,98,99
First is the normal one,Second one formed by reversing or inverting the first,the third is formed by rotating the first by 90 degrees.All three give the same total 264 all around.They are shown below-
96,11,89,68
88,69,91,16
61,86,18,99
19,98,66,81
Second one-
16,68,99,81
91,89,18,66
88,96,61,19
69,11,86,98
Third one-
18,99,86,61
66,81,98,19
91,16,69,88
89,68,11,96

Reverse a magic square

I  show below a magic square with totals 264 all around-
96,11,89,68
88,69,91,16
61,86,18,99
19,98,66,81
Now reverse the grid.,and make a small change,you will get a new magic square having the same totals all around-
18,99,86,61
66,81,98,19
91,16,69,88
89,68,11,96

Inflation number 72

This is an issue involving inflation.
Suppose you find that the cost of a product or service uniformly goes up every year by 10%.
Will you be able to find out when the cost or service becomes double?
The answer is 7.2 years,the period 7.2 being one tenth of 72.
If the cost goes up every year by 5%,the period will be 14.4 years,the same being one-fifth of 72
Using the number 72,you can find the period for any percentage of increase.
Will you be able to work out how this number 72 is involved?.

Repeating sequence

I am giving below a few initial terms of a sequence-
0,0,0,1,0,2,1,0,3,2,1,4,0,5,3,,2,6,1,7,4,0,8,5.........
The surprising feature of this sequence is that if  you delete the first occurrence of each digit,the original sequence will show up again.
I am showing below the position after deleting the first occurrence of each digit  ,the  deleted digits shown in brackets for ready check-
(0),0,0,(1),0,(2),1,0,(3),2,1,(4),0,(5),3,2,(6),1,(7),4,0,(8),5.....
Can you find out the further digits/numbers in the original sequence so that this property remains in force?

Cyclic number-16 digits-More information

In an earlier blog I had shown a cyclic number of 16 digits reproduced below-
0588235294117647
I had shown that multiplication of this number successively by 12,8,11,13,3,2,7,16,5,9.6,4,14,15 and 10  makes the last digit at right move to the left side successively.
Let me now tell you how this sequence of multipliers could be found.
The cyclic number is actually found by working out the reciprocal of 17,which could be treated as a generator of the same.The first number in the sequence viz 12 is the most important multiplier.Every subsequent multiplier is found by repeatedly multiplying the previous one by 12.From every result of multiplication you have to however deduct 17 as many times as necessary.
Thus the second multiplier is 12*12-17*8=                                         144-136=8
Third multiplier is                  8*12-17*5=                                            96-85= 11
Fourth                                11*12-17*7=                                          132-119=13
Fifth                                   13*12-17*9=                                          156-153=3 etc etc
You can go upto the multiplier 7 like this .The remaining multipliers are those found by deducting successively those found earlier from 17...Viz17-1=16,   17-12=5,    17-8=9     17-11=6 etc etc
I will inform you in another blog how the first number 12 can be used to find the subsequent multipliers in another way

More surprises-magic squares-3/3 cells

I had shown some data relating to 3/3 cell magic squares in my first blog.
I am now revealing more information
The digits in the rows and columns were as follows-
4,9,2
3,5,7
8,1,6
The sum of the squares of the numbers formed by the digits in each row and each column expressed in two different ways were shown by me to be equal..
The same position is revealed even when the digits in the diagonal and non-diagonal cells are taken into account as shown below-(S means the square of the number)
Relating to diagonal 4,5,6-,...S(456)+S(978)+S(231)=S(654)+S(879)+S(132)=1217781.
Similarly relating to diagonal 2,5,8-     S(258)+S(693)+S(714)=S(852)+S(396)+S(417)=1056609