19th May 2024

Numbers too can be ‘narcissistic’

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What is the commonality between – 153, 370, 371, and 407?

We can observe that,

13 + 53 + 33 = 1 + 125 + 27 = 153

33 + 73 + 03 = 27 + 343 + 0 = 370

33 + 73 + 13 = 27 + 343 + 1 = 371

43 + 03 + 73 = 64 + 0 + 343 = 407

Similarly, we have three such four-digit numbers, 1634, 8208 and 9474.

14 + 64 + 34 + 44 = 1 + 1296 + 81 + 256 = 1634

84 + 24 + 04 + 84 = 4096 + 16 + 0 + 4096 = 8208

94 + 44 + 74 + 44 = 6561 + 256 + 2401 + 256 = 9474

There are three such five-digit numbers, 54748, 92727 and 93084 and one six-digit number, 548834. The readers may verify. Such numbers are called Narcissistic Numbers. The highest possible number of digits for which we can get a Narcissistic Numbers is 39. There are two such numbers –

115132219018763992565095597973971522400 and 115132219018763992565095597973971522401

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