perplexus.info :: Numbers : What is OCTOBER?

What is OCTOBER? (Posted on 2024-08-14)

The letters represent a different base ten digit from 0 to 9. None of the numbers can denote a leading zero.
Given that:
O+CTO = BER, and:
OCTOBER is divisible by both 3 and 7.

What is the value of OCTOBER?

No Solution Yet Submitted by K Sengupta

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Mod 3 analysis (for what it is worth)

| Comment 1 of 2

An integer is divisible by 3 if and only if the sum of its digits is divisible by 3.

Therefore,

OCTOBER is divisible by 3

=> O+CTO+BER is divisible by 3

=> BER + BER is divisible by 3

=> BER is divisible by 3

Then O + CTO is divisible by 3

=> O+CT+O is divisible by 3

=> O = CT (mod 3)

Posted by Steve Herman on 2024-08-14 08:08:11

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