A. Maximize the Last Element #
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B. AND Reconstruction #
Idea
Find minimum possible value of each $A_i$, then check if it gives you $B$
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C. Absolute Zero #
Hint
Can you decrease maximum by half in one operation?
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D. Prime XOR Coloring #
Hint 1
The answer is always <= 4.
Hint 2
If $u$ and $v$ both have same remainder when divided by 4, then $u \oplus v$ is a multiple of $4$.
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Bonus: How to write checker for D?
E. Coloring Game #
Hint 1
What should be alice strategy?
Hint 2
Alice should always chose color 1 and 2.
Hint 3
When can Bob color all the vertices using 2 colors?
Hint 4
Bob can color all the vertices using just 2 colors if graph is Bipartite graph
Hint 5
Play as Bob if graph is Bipartite graph and Alice otherwise.
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F. Triangle Formation #
Hint
The answer is always YES, if $R-L > C$ for some $C$