
#920209  11/02/08 09:15 PM
Can anyone figure this out? Uncanny!

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Grandpianoman
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#920215  11/03/08 09:04 PM
Re: Can anyone figure this out? Uncanny!

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currawong
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Originally posted by zp3929: so how do they gee the correct symbol then? In any one trial, your answer will always be a multiple of 9. All multiples of 9 always have the same symbol in any one trial. Therefore, in any trial the gopher just says what that symbol is and he'll be right. In the next trial, the gopher says what the symbol allocated to all multiples of 9 that time is, and he'll be right again, because once again your answer will always be a multiple of 9.
Du holde Kunst...



#920217  11/03/08 10:52 PM
Re: Can anyone figure this out? Uncanny!

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currawong
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Originally posted by keystring: Unless you're lousy at math. Then the gopher gets it wrong. So that's how I managed to fool the gopher! I knew being lousy at maths must have some advantages!
Du holde Kunst...



#1806955  12/16/11 12:32 AM
Re: Can anyone figure this out? Uncanny!
[Re: Tmoose]

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Kazari
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I couldn't resist: Here is an explanation/sketch of proof ( a formal proof would require notation that is more difficult to type out, along with some special cases)
Example: Original number 24971, new number 17249. The difference is 7722 whose sum of digits is 18.
7722 also equals (21)*10000+ (47)*1000 +(92)*100 +(74)*10 +(19)*1.
The sum of digits = (21) +[1+10((47))] + (92)+(74)+[1+10((19))] = 2*9 + [(21) + (47) +(92)+(74)+(19)] = 2*9 +(2+4+9+7+1) (1+7+2+4+9)= 2*9 +0
In the first line of the sum of digits expression, the negative expressions in red contributes to the sum of digits in a different way than each positive expression. Essentially that is because to subtract a number from say the thousandth place, you subtact 1 from the tenthousandth place and then take 10  your number, the normal way subtraction is done. The next part of a proof relies on the fact that a permutation of the digits of the original number does not change the sum of the digits, that is, the sum of digits in 24971 and 17249 is the same, hence the expression in blue is 0.
Since the difference between the original number and the new number is always a multiple of 9, and that any multiple of 9 always has sum of digits 9, the sum of digits of the difference is always 9.
Working on:
Adagio, Concerto in D minor, movement II (BachMarcello) Nuvole Bianche (Ludovico Einaudi) Croatian Rhapsody (Tonci Huljic) Jingle Bell Rock (??)




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