Why always.... 6,Numbers are amazing...I Love

[mathspassion]

Numbers are amazing ,if we deep study about we get a lot miracle which we have to bring out ,in this view one more article see and observe why is it so……….why always 6.

(2,2,3....2,2,3......)

 

123-----1+2+3=6=0+6=6

456-----4+5+6=15=1+5=6

789-----7+8+9=24=2+4=6

101112----10+11+12=33=3+3=6

131415-----13+14+15=42=4+2=6

161718-----16+17+18=51=5+1=6

192021-------19+20+21=60=6+0=6

222324------22+23+24=69=15=1+5=6

252627------25+26+27=78=7+8=15=1+5=6

282930-----28+29+30=87=8+7=15=1+5=6

313233------31+32+33=96=9+6=15=1+5=6

343536------34+35+36=105=1+0+5=6

373839------37+38+39=114=1+1+4=6

404142------40+41+42=123=1+2+3=6

434445------43+44+45=132=1+3+2=6

464748------46+47+48=141=1+4+1=6

495051-----49+50+51=150=1+5+0=6

525354-----52+53+54=159=1+5+9=15=1+5=6

555657-----55+56+57=168=1+6+8=15=1+5=6

585960----58+59+60=177=1+7+7=15=1+5=6

616263----61+62+63=186=1+8+6=15=1+5=6

646566----64+65+66=195=1+9+5=15+1+5=6

676869----67+68+69=204=2+0+4=6

707172----70+71+72=213=2+1+3=6

737475---73+74+75=222=2+2+2=6

767778---76+77+78=231=2+3+1=6

798081---79+80+81=240=2+4+0=6

828384---82+83+84=249=2+4+9=15=1+5=6

858687---85+86+87=258=2+5+8=15=1+5=6

888990---88+89+90=267=2+6+7=15=1+5=6

919293---91+92+93=276=2+7+6=15=1+5=6

949596---94+95+96=285=2+8+5=15=1+5=6

979899---97+98+99=294=2+9+4=15=1+5=6

100101102--100+101+102=303=3+0+3=6

103104105--103=104+105=312=3+2+1=6

106107108—106+107+108=321=3=2+1=6

109110111—109+110+111=330=3+3+0=6

 

copyright to PiyushGoel

[DrKrettin]

Have you tried that same in a different base, say octal and hexadecimal? Is the number 6 still as magical?

[imatfaal]

Not magical at all. Simply explained.

 

1. The initial three digits equal 6

2. Each subsequent set of digits is 9 more

3. In decimal notation the process of adding 9 can be seen as adding 1 to the tens column and subtracting 1 from units column

4. Adding 1 and subtracting 1 will always leave the digit sum as the same as the previous answer - 6

 

If you started with 2,3,4 every triple would eventually add to 9, and if you started with 3,4,5 every triple would add to 3.

 

Neither new, nor interesting

[Commander]

 

Still thinking !

100110021003 produces 9

 

234 produces 9

 

345 produces 3

 

Well only in the order listed by you that is true

 

That is any three consecutive numbers adding to 6

 

It only happens if the first number of the series say N is such that

 

N-1, N-4 or N-7 is a multiple of 9 and the rest is simple as explained by imatfaal

Edited April 12, 2017 by Commander

[Country Boy]

Look up "casting out nines": https://en.wikipedia.org/wiki/Casting_out_nines

 

(Or "casting out "n-1"s for base n.)

[mathspassion]

we took here 123,456.....

not 123,234,345.....mean no repaeting of digit.

 

my question is why for this........ always 6(sum of digits) at the end.

 

For example

123=6

234=9

345=12=3

456=15=6

567=18=9

678=21=3

789=24=6 at the end sum of digits repaeating.

 

and if we do with one more example

 

12=3

23=5

34=7

45=9

56=11=2

67=13=4

78=15=6

89=17=8

910=19=10=1

1011=21=3 at the end sum of digitis repeating.

[Sriman Dutta]

For numbers like 454647, we are considering three consecutive integers as parts of the number. So 454647 has three consecutive integers- 45,46 and 47. We can represent them as 10n + a, 10n+(a+1) and 10n+(a+2); where n is the tens digit ( here n=4) and a is the ones digit, three consecutive integers, and so a, a+1 and a+2. If we add, then

10n + a

10n + (a+1)

10n + (a+2)

_______________

30n + 3a +3 = 3(10n + a + 1)

So its a multiple of 3.

[imatfaal]

...

my question is why for this........ always 6(sum of digits) at the end.

 

...

 

And I answered your question. The first three numbers 1,2,3 add to six (both in normal summation and digit-wise summation obviously). Each success triplet is 9 bigger* - if you add 9 to any number in the decimal system the digit sum remains the same (because you decrease the units column by one and increase the tens, or a higher column by one). So if the first sum is 6 then all subsequent sums will be 6. I even showed that different starting seeds would give repeated 3s and repeated 9s. This is well known, not surprising, and no mystery

 

 

* this is simple the first triplet adds 1+2+3, the second is (1+3)+(2+3)+(3+3) = 1+2+3 +3+3+3 = 1+2+3+9; it is clear this continues

[Sriman Dutta]

By the way, who is Piyush Goel ?

[mathspassion]

ok let see

[mathspassion]

sriman bhai pata laga who is piyush goel

[Unity+]

Neither new, nor interesting

Not new? Maybe

 

Not interesting? I would beg to differ

[imatfaal]

Not new? Maybe

 

Not interesting? I would beg to differ

 

Something which can be so easily explained as an artifact of the number system is not that interesting in my opinion. But then most of the stuff I find interesting I don't really understand

[mathspassion]

if you have new post mere bhai....(unity & imatfall). give new to the world...........

friends who do not put right name i think they are fake you both of that type person you know....

 

likhne aur sochne mein bahut difference hain........

[Bender]

if you have new post mere bhai....(unity & imatfall). give new to the world...........

friends who do not put right name i think they are fake you both of that type person you know....

 

likhne aur sochne mein bahut difference hain........

mjqksdf ysoidfyo ejrklno mlsiur...

[mathspassion]

sriman dutta i got some while searching piyush goel on google i think he has lot work done in mirror image writing/mathematics/making caricatures etc.........