Decimal fractions puzzle-Rejoinder

Though it is a very easy puzzle, no one has given a reply so far.
Let me explain the method.
For the 3 fractions x,y and z ,I had mentioned that x(1),y(1) and z(1) are the integer parts and x(2),y(2) and z(2) the decimal parts.
So you can see that x=x(1)+x(2).....y=y(1)+y(2)     and z=z(1)+z(2).
I had given 3 equations x+y(1)+z(2)=4.2
.                                  y+z(1)+x(2)=3.6 and
                                   z+(x(1)+y(2)=2.0
Adding all 3 together we get x+y+z+x(1)+y(1)+z(1)+x(2)+z(2)=9.8 or because x=x(1)+x(2) ..etc
we have 2(x+y+z)=9.8 or x+y+z=4.9
Deducting the first equation from this we will have x+y+z-x-y(1)-z(2)=4.9-4.2=0.7 which means
y(2)+z(1)=0.7...This further means that z(1)=0 and y(2)=0.7
Similarly deducting the 2nd and 3rd equations we will get x(1)=1 and z(2)=0.3 and y(1)=2 and x(2)=0.9
Thus the 3 fractions are 1.9,....2.7 ... 0.3.

A number sequence to be filled

You are required to find the next number in the sequence 10,9,60,90,70,66
You will find it difficult to find the number if you tackle it as a mathematical issue
The actual way is to tackle it as an alphanumeric issue.
10 is the highest number which can be written in 3 alphabets
9 similarly the highest which can be written in 4 alphabets.
Likewise 60,90,70,66 -those which are highest as could be written in 5,6,7 and 8 alphabets.
Now go ahead and find the highest number which could be written in 9 alphabets.

Decimal Fractions Puzzle

Let x,y and z be 3 decimal fractions.The integral portion in each is denoted by x(1),y(1) and z(1) and the fractional portion by x(2),y(2) and z(2) respectively.
If x+y(1)+z(2)=4.2,y+z(1)+x(2)=3.6 and z+x(1)+y(2)=2,Find the values of  all the 3 fractions..

Divisibility-Rejoinder

My previous blog on this topic dealt with squares and their divisibilities-
1)About the square numbers divisible by 392-
First find the nearest square divisible by 392-It is 2*392=784(square of 28)
You must now multiply 784 by any other square number to find all squares divisible by 392-
like 4,9,16,25,36,49 64,81,100,121,144,169 etc to find the nearest square above or below any limit.
Multiplication of 784 by 144 gives you the nearest square above 100000,while multiplication by 121 gives you the square nearest below 100000
2)Multiplication of 784 by 225 gives the nearest square above 150000
3)Regarding divisibility  by 1323,we find its factors as 3,3,,3,7, and 7.So you must multiply by 3 to make it a square viz 3969-Square of 63.You can then decide which square you have to  multiply with 3969,to find the squares above or below any limit.