### Brain Teasers

# Liars

Twelve men are in a room, some of them always tell lies, while the others always tell the truth.

The first man says: "None of us is a truthteller."

The second man says: "At most one of us is a truthteller."

The third man says: "At most two of us are truthtellers."

...

The twelfth and last man says: "At most eleven of us are truthtellers."

Who are the liars?

The first man says: "None of us is a truthteller."

The second man says: "At most one of us is a truthteller."

The third man says: "At most two of us are truthtellers."

...

The twelfth and last man says: "At most eleven of us are truthtellers."

Who are the liars?

### Hint

It's OK to use trial and error, however, there might exist better methods.### Answer

If there are exactly N liars, then the last N men are truthtellers, leaving the first (12-N) men to be liars.Therefore, N=12-N, N=6. The first 6 men are liars, and the last 6 men are truthtellers.

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