Problem 11.5. At the call of the voivode, 55 soldiers arrived: archers and swordsmen. All of them were dressed either in golden or black armor. It is known that swordsmen tell the truth when wearing black armor and lie when wearing golden armor, while archers do the opposite.

- In response to the question "Are you wearing golden armor?", 44 people answered affirmatively.
- In response to the question "Are you an archer?", 33 people answered affirmatively.
- In response to the question "Is it Monday today?", 22 people answered affirmatively.

How many archers in golden armor came at the voivode's call?
Answer: 22.

Solution. To the first question, affirmative answers will be given by archers in gold armor and archers in black armor, that is, all archers.

To the second question, affirmative answers will be given by archers in gold armor and swordsmen in gold armor, that is, all soldiers in gold armor.

To the third question, affirmative answers will be given either by swordsmen in gold armor and archers in black armor (if it is not Monday), or by swordsmen in black armor and archers in gold armor (if it is Monday). In the first case (if it is not Monday), we will sum the number of affirmative answers to all three questions. This will result in double the number of swordsmen in gold armor plus double the number of archers, i.e., an even number, but according to the condition, it equals \(22+33+44=99\) and is odd, which is a contradiction. Therefore, to the third question, affirmative answers were given by swordsmen in black armor and archers in gold armor.

Now, let's sum the number of affirmative answers. This will result in triple the number of archers in gold armor plus the number of all others (once each). Then, if we subtract the total number of soldiers from this number, we get double the number of archers in gold armor, which needs to be divided by two:

\[
\frac{22+33+44-55}{2}=22
\]