Who's next? Part II

Number Theory Level 2

Given a sequence of numbers 1 , 8 , 7 , 4 , 5 , 6 , … 1, 8, 7, 4, 5, 6,\ldots , what will be the next number?

1 2 9 6 8 5 3 0

Hobart Pao by Hobart Pao , 23, USA

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1 solution

Hobart Pao
May 30, 2016

The pattern is that these are the units place digits of the first 6 perfect cubes. So, the next number in the sequence should be 3 \boxed{3} because 7 3 = 343 7^3 = 343

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I suppose part III could be the sequence of perfect fourth powers: 1 , 6 , 1 , 6 , 5 , 6 , 1 , 6 , 1 , . . . 1,6,1,6,5,6,1,6,1, ... , with the next term being 0 0 . Might be able to catch a few people out with that one. :)

Brian Charlesworth - 5 years ago

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Well, there are possibly different explanations, like "repeating 1,6,1,6,5,6" and so the next value is 6.

Calvin Lin Staff - 5 years ago

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