# The Strange Mind Of Eureka Blip Puzzle - Solution

### The Puzzle:

Welcome to the strange mind of Eureka Blip.

He does not always think the same way as we do, but he does always have his own logical set of rules. One of his favourite tricks is to say the opposite of what he really means. Recently I had a conversation with him, which went like this:

"Good morning, Eureka, how are you?"

"Go away. I feel absolutely dreadful."

"What are you thinking about today?"

"I am not thinking of any number at all."

"Is your number less than 50?"

"No. It is greater than 50, and it is a prime number."

"Is it less than 26?"

"Yes, and it is an even number."

"And it's not a square number?"

"Correct."

"Thank you, Eureka. Goodbye."

"Please. Hello."

What was Eureka Blip thinking of?

He does not always think the same way as we do, but he does always have his own logical set of rules. One of his favourite tricks is to say the opposite of what he really means. Recently I had a conversation with him, which went like this:

"Good morning, Eureka, how are you?"

"Go away. I feel absolutely dreadful."

"What are you thinking about today?"

"I am not thinking of any number at all."

"Is your number less than 50?"

"No. It is greater than 50, and it is a prime number."

"Is it less than 26?"

"Yes, and it is an even number."

"And it's not a square number?"

"Correct."

"Thank you, Eureka. Goodbye."

"Please. Hello."

What was Eureka Blip thinking of?

### Our Solution:

Let's "translate" Eureka's words so that they say what he means:

"Good morning, Eureka, how are you?"

"Come and join me. I feel fine."

"What are you thinking about today?"

"I am thinking of a number."

"Is your number less than 50?"

"Yes. It is less than 50, but it is not a prime number."

"Is it less than 26?"

"No, but it is an odd number"

"And it's not a square number?"

"Wrong. It IS a square number."

"Thank you, Eureka. Goodbye."

"Thank you. Goodbye."

There is only one square number between 26 and 50 which is odd, and that's the answer:

Eureka was thinking of the number 49.

"Good morning, Eureka, how are you?"

"Come and join me. I feel fine."

"What are you thinking about today?"

"I am thinking of a number."

"Is your number less than 50?"

"Yes. It is less than 50, but it is not a prime number."

"Is it less than 26?"

"No, but it is an odd number"

"And it's not a square number?"

"Wrong. It IS a square number."

"Thank you, Eureka. Goodbye."

"Thank you. Goodbye."

There is only one square number between 26 and 50 which is odd, and that's the answer:

Eureka was thinking of the number 49.

Puzzle Author: Stephen Froggatt

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