Solution: The Enthusiastic Islanders Riddle

Solving the “Enthusiastic Islanders” Riddle

 

First try solving this puzzle on your own and comment in the post -> The Two-GuardsRiddlThe Enthusiastic Islanders Riddlee

 

⚠️ The Riddle:

On a strange island, 10 people are either half-hearted or enthusiastic.

A visitor asks them all: ‘How many enthusiastic people are here?’ 

They reply: 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. 

Half-hearted folks never exaggerate. 

Enthusiastic folks never downplay. 

So… 

How many are actually enthusiastic?

 

🧩 Answer?

 6

 

💡 Explanation:

Let’s break it down:

Let’s call the actual number of enthusiastic people E.

• Enthusiastic people are optimistic — they’ll never say fewer than E.
• Half-hearted folks are pessimistic — they’ll never say more than E.

So anyone saying less than E must be half-hearted.
Anyone saying more than E must be enthusiastic.

We test all possible E values from 3 to 12 (the answer range), and count:

• How many said less than E → must be half-hearted
• How many said more than E → must be enthusiastic

We look for the number where:
Number of people who said < E + Number who said > E = 10 – 1 (excluding the one who said E)
Then see if the count of enthusiastic and half-hearted people add up correctly with that split.

When E = 6, here's what we get:

• Residents who said <6: 3, 4, 5 → 3 people → must be half-hearted
• Residents who said >6: 7, 8, 9, 10, 11, 12 → 6 people → must be enthusiastic
• One person said exactly 6 → could be either

So total enthusiastic = 6 (consistent).
Total half-hearted = 3 (also works).

🎯 Bingo! E = 6 is the only number that satisfies this.

 

🌱 Real-Life Lesson?

Sometimes, the truth lies right in the middle — not in the loudest voices or the lowest whispers, but in what’s consistent with reality. People may overhype or downplay, but math? Math’s got receipts. 📊 

So next time opinions are flying around — try being the one who calmly does the math. You might just be the real enthusiast. 😉

 

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