Can someone solve this tasks from a competition?

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Nekemtenee

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Oct 29, 2014
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My english isn't really good, so I will make a picture. There is a chart with 4 arrays. In the first array, there are the integers from 1 to 2000. In the arrays below you sum the digits. for example: if the number in the first array is: 123 the sum is: 1+2+3=6 so in the third array and the fourth array is 6 also... http://i.imgup.hu/p4SuC8.pngThe question is how many 1s will be in the fourth array? for example 1126 is a good answer because: 1+1+2+6=10 then in the 3rd array: 1+0=1 4th: 1+0=1
 
Nekemtenee said:
My english isn't really good, so I will make a picture. There is a chart with 4 arrays. In the first array, there are the integers from 1 to 2000. In the arrays below you sum the digits. for example: if the number in the first array is: 123 the sum is: 1+2+3=6 so in the third array and the fourth array is 6 also... http://i.imgup.hu/p4SuC8.pngThe question is how many 1s will be in the fourth array? for example 1126 is a good answer because: 1+1+2+6=10 then in the 3rd array: 1+0=1 4th: 1+0=1
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An interesting question - hope you get an answer and, more importantly, a technique (some techniques) for getting the answer which don't become super involved.
 
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