perplexus.info :: Numbers : Arithmetic Sequence Crossed Digital Root Puzzle

Arithmetic Sequence Crossed Digital Root Puzzle (Posted on 2023-02-16)

A, B, and C are three consecutive integer terms (in this order) of an arithmetic sequence with nonzero common difference d.
Define:
• x = A³+B³+C³
• d(x) as the digital root of x.

Determine d(x), given that x is NOT a multiple of 3.

See The Solution Submitted by K Sengupta

Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Unless ...

| Comment 2 of 3 |

I was thinking the same thing as Steve Herman.

Unless ...

{A, B, C} = {-1, 0, 1}

so x = 0

And although 0 is equivalent to 0 mod 3,

technically, 0 is not a multiple of 3.

I guess it comes down to semantics.

Posted by Larry on 2023-02-16 09:00:49

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