The value of n must be among those numbers such that the ones digit of n^n be n.Now, ones digit of 3^3 = 9,so, n doesn't equal 3.Now, If n = 1, then, 1^1 = 1 ,so, n can be 1.Similarly, the all values of n among 1 and 9 can be 1,5,6 and 9.

Lakshya leap - can you please give the reason why n^n needs to be n.

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Laksha Leap answered this

Here is the condition. if n^n ends with digit n and if, then, we subtract n from n^n , then, the resultant number must will have 0 in ones place.For instance: if n = 5, then, 5^5 - 5 = 3125 - 5 = 3120 (end digit is 0) and since, the end digit will be 0, so, the resultant number must be the multiple of 10.