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Yes.

Choose any three consecutive counting numbers.

The first number is the second number subtract 1

The third number is the second number add 1

Adding the three numbers together is the same as adding:

(the second number subtract one) plus the second number plus (the second number add one).

The "subtract one" and "add one" cancel each other out to leave the sum as:

the second number plus the second number plus the second number

Which is the same as 3 times the second number, ie the sum is a multiple of 3 and so is divisible by 3.

For example:

10 + 11 + 12 = (11 - 1) + 11 + (11 + 1) = 11 - 1 + 11 + 11 + 1 = 11 + 11 + 11 + (1 - 1) = 11 + 11 + 11 + 0 = 11 + 11 + 11 = 3 x 11

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Q: Is the sum of any three consecutive counting numbers always divisible by 3?
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