At BOSS we spend a lot of time thinking about how to keep messages secret. But sometimes secrecy is not the problem.

Sometimes you just want to make sure the message that arrives is the message that was sent.

Radio links can be noisy. A burst of interference, a faulty circuit or a damaged storage device can turn a 0 into a 1, or a 1 into a 0. If the message is important, merely knowing that something has gone wrong may not be enough. It would be much more useful if the message itself contained enough information to tell you where the error was.

One of the older BOSS field systems does exactly that.

The puzzle

Every message consists of seven bits, numbered from 1 to 7.

Four of them carry the actual information. The other three help us detect mistakes.

A correctly transmitted message obeys three bit check rules:

Bit checks	GOLD	BLUE	RED
1	✓	✓
2	✓		✓
3		✓	✓
4	✓
5		✓
6			✓
7	✓	✓	✓

The four information bits are in positions 1, 2, 3 and 7.

A message has just arrived but unfortunately exactly one of the bits is wrong!

	1	2	3	4	5	6	7
Received bit	1	1	1	1	0	0	1

The operator knows that exactly one bit was changed during transmission.

Your job is to repair the message.

Which bit was changed?

What was the original seven-bit message?

And what four-bit information was actually being sent?

Need a hint?

If you need a hint then click here to reveal it,, but we would really suggest trying the puzzle on your own first!

Hint 1

Test the received message against each of the three rules.

Which checks pass, and which fail?

Hint 2

Exactly one bit is responsible for everything that has gone wrong.

Look for a bit that belongs to both of the failed checks, but does not belong to the check that passed.

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