Tag: math & puzzles

To determine the next term in this sequence, we need to analyze the pattern and rules that govern its progression.

The sequence starts with 1. The next term, 11, can be described as "one 1," since it consists of two consecutive 1s. The following term, 21, can be described as "two 1s," as it consists of one 2 and one 1.

Continuing this pattern, the next term is 1211, which can be described as "one 2, one 1."

The pattern continues in this manner, where each term is described in terms of the counts of consecutive digits in the previous term.

Now, let's go through each option and determine which one follows this pattern:

A. 112221: This option does not follow the pattern. It does not describe the counts of consecutive digits in the previous term.

B. 131221: This option does not follow the pattern. It does not describe the counts of consecutive digits in the previous term.

C. 312211: This option follows the pattern. It describes the counts of consecutive digits in the previous term (one 3, one 1, two 2s, one 1).

D. 221221: This option does not follow the pattern. It does not describe the counts of consecutive digits in the previous term.

Therefore, the correct answer is C. 312211.

To solve this question, the user needs to know the definitions of Knights, Knaves, and Normals, and how they behave when they are asked questions. The user must also understand the context of the inhabitant's statement and analyze it to determine their true identity.

Now, let's go through each option and explain why it is right or wrong:

A. Knight: This option cannot be correct since Knights always tell the truth, so if the inhabitant was a Knight, their statement "I'm no Knight" would be a lie, which contradicts the definition of a Knight.

B. Knave: This option cannot be correct since Knaves always lie, so if the inhabitant was a Knave, their statement "I'm no Knight" would be a lie, which contradicts the definition of a Knave.

C. Normal: This option is correct. Normals sometimes tell the truth and sometimes lie, so the inhabitant's statement "I'm no Knight" could be true or false. If the inhabitant is a Normal and is telling the truth, it means they are not a Knight, which would make them either a Knave or a Normal. If the inhabitant is a Normal and is lying, it means they are a Knight, which again would make them not a Knight. Therefore, the inhabitant must be a Normal.

D. None: This option is not correct since we have already determined that the inhabitant is a Normal.

The Answer is: C. Normal