Competition problem — Combinatorics

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Combinatorics Difficulty 5.9 AIME, harder Find the answer

[8.1] In a competition, three problems $A, B, C$ were given. It is known:
(i) Among all the participating students, 25 people each solved at least one problem;
(ii) Among the students who did not solve problem $A$ , the number of students who solved problem $B$ is twice the number of students who solved problem $C$ ; $\square$
(iii) Among the students who solved problem $A$ , the number of students who only solved $A$ is one more than the number of students who solved other problems as well;
(iv) Among the students who only solved one problem, half did not solve problem $A$ . How many students only solved problem $B$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

None

Translate the text above into English, please retain the original text's line breaks and format, and output the translation result directly.

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None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.