$\begin{array}{ll}{\left[\begin{array}{l}\text { Rebus } \\ \text { [Decimal Number System] }\end{array}\right]}\end{array}$

A number was added to the sum of its digits, and the result was 2014. Provide an example of such a number.

## Answer

1988 or 2006.

On an island, there are 1234 inhabitants, each of whom is either a knight (who always tells the truth) or a liar (who always lies). One day, all the inhabitants of the island paired up, and each one said about their partner: "He is a knight!" or "He is a liar!" Could it have turned out that both phrases were said an equal number of times?
Suppose the described situation is possible. Then, each of the phrases was said $1234: 2=617$ times.

There are only three possible types of pairs: two knights; two liars; a knight and a liar. In pairs of the first and second types, each said: "He is a knight!", while in pairs of the third type, each said: "He is a liar!". Thus, each phrase was said an even number of times, which contradicts the fact that they should be 617.

## Answer

It could not have.