Add them all!

Number Theory Level 3

N 0 = 563 ⟹ N 1 = 5 + 6 + 3 = 14 ⟹ N 2 = 1 + 4 = 5 N_0 = 563 \implies N_1 = 5+6+3 =14 \implies N_2 = 1 + 4 = 5

As shown in the example above, how many integers are there between 1 and 1000 such that repeated sum of their digits will eventually lead to 5?


The answer is 111.

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Md Zuhair by Md Zuhair , 20, India

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1 solution

Md Zuhair
Sep 15, 2016

The numbers are 5 , 14 , 23 ... And they are in A P AP . Hence the last number is 995 995 . Then 990 = 9 ( n − 1 ) 990=9(n-1) or n = 111 111

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@Pi Han Goh can we take the number 5 in these series ? Then my answer will be correct.

Md Zuhair - 4 years, 8 months ago

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