Jump to content
mathspassion

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

Recommended Posts

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

Share this post


Link to post
Share on other sites

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

Share this post


Link to post
Share on other sites

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

Share this post


Link to post
Share on other sites

:)

 

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 by Commander

Share this post


Link to post
Share on other sites

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.

Share this post


Link to post
Share on other sites

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.

Share this post


Link to post
Share on other sites
...

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

Share this post


Link to post
Share on other sites

Neither new, nor interesting

Not new? Maybe

 

Not interesting? I would beg to differ :P

Share this post


Link to post
Share on other sites

Not new? Maybe

 

Not interesting? I would beg to differ :P

 

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

Share this post


Link to post
Share on other sites

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........

Share this post


Link to post
Share on other sites

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...

Share this post


Link to post
Share on other sites

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.........

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.