## Sunday, March 29, 2015

### Finding Patterns Multiplication by 19 the harder way

```

for i in range(1,30):
print (str(19)+"*"+str(i)+"=",19*i)
print "difference=",((19*(i+1))/10 - (19*i)/10)
print("=======================================")

"""
Multiplication by 19 ==> The harder way

Many would suggest ==> 1| 3|5| 7|9|11| 13| 15| 17|19  ==> odd numbers(1,3,5..)
9| 8|7| 6|5|4 | 3 | 2 | 1 | 0  ==> numbers from 9,8,7....
------------------------------
19,38,57,76.......

It's easy but you should write it down

This is for kids ==> Rather than by heart just know that
19*n=(2*n)-1 ==> This will be first digit

From the observations

19*36=??
Once you know 19 table it's not a big deal but sometime for starters it's a mess to remember numbers.

I assume you know 2 table;i assume you know compliment of a number;
for compliment pairs ==> (1,9),(2,8),(3,7),(4,6),(5,5),(6,4),(7,3),(8,2),(9,1)

Ex : 19* x = (2x-1)[compliment of x]

19*36==> (2*3 - 1)7 [compliment of 3 is 7] and (2*6 -1)4 [compliment of 6 is 4]==> 57 114 ==> 11 carry over ==> 57+11 =68==>684

"""

```

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