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The number formed when the integers 1, 2, 3 • • • 2021 are strung together in increasing order, 12345678•••20192021 is transformed into a new number through the following algorithm: The first digit is taken, doubled, then added to the second digit. This sum is then doubled, and added to the third digit. This value is doubled, and added to the fourth digit, until we use up all of the digits, and a new number is formed. We repeat this process on the new number, and then on the number that is formed from the new number, continuing until we reach a one digit number. Find this one digit number.

 Aug 24, 2022
 #1
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Not sure if I understand your question!

 

Let us try a small number: 12345

2 x 1 + 2=4

2 x 4 + 3 = 11

2 x 11 + 4 = 26

2 x 26 + 5 = 57.  Now, what is next? Are you supposed to do the same with: 4, 11, 26, 57 ?? If so, this will take a long time without a computer code!. 19, 64, 185 and this becomes: 102, 389 and this becomes: 593 and this becomes: 79 and this becomes: 23 and this becomes: 7

 

Does this make sense to you? It makes no sense to me !!

 Aug 24, 2022
 #2
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I think it's asking you to do the same 57, which would turn into 5*2+7=17, and then do it on 17, which would turn into 1*2+7=9.

RainbowSquirrel53  Aug 24, 2022
 #3
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If 57 was the FINAL result, it would make sense. But your question says: Take this last sum, double it and add it to the next number, which would be: 57 x 2 + 6=120, and double this to: 120 x 2 + 7=247......and if you keep doing this, then the 2021st term will be a HUGE number about 610 digits long!!!

Guest Aug 24, 2022
 #4
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I don't understand what you're doing there. Once you get 57, you basically start over the process. You do the same thing you did to 12345 to 57.

RainbowSquirrel53  Aug 24, 2022
 #5
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Remember that we used: 12345 as a very small example!! But the number in your question goes on and on like this: 12345678910111213141617181920........201920202021. You have almost 7000 digits to do!!!!

Guest Aug 24, 2022
 #6
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that's why I'm asking this question! How do you do it?

RainbowSquirrel53  Aug 24, 2022

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