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


mathspassion

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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

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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

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:)

 

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
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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.

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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.

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...

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

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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

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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........

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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...

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