Explain this math puzzle using visual whiteboard steps, calm narration, and handwriting-style animation. Reveal only one idea at a time. Do not show the full board at once. Let each step appear only after the narration. Keep a thoughtful pace.
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🎯 Problem:
"There are 60 animals. Some are chickens (2 legs), some are dogs (4 legs).
Together, they have 194 legs.
How many chickens and how many dogs?"
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🧠 Strategy:
Use **Hypothetical Reasoning — Strategy #01**, also called **Assumption-Based Modeling**.
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🔹 Step 1: Set the scene.
Narrate first:
"You walk into a farm…
Chickens clucking… dogs barking…
Someone hands you this puzzle."
Then write:
• "60 animals" (top left)
• "194 legs" (below)
• "🐔 = 2 legs 🐕 = 4 legs" (right)
• "Q: Chickens? ___ Dogs? ___" (center)
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🔹 Step 2: Assume all are chickens.
Narrate:
"Let’s assume every animal is a chicken.
Even the ones... that clearly bark."
Then write:
• "Assume all chickens → 60 × 2 = 120 legs"
Pause 2 seconds.
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🔹 Step 3: Compare to reality.
Narrate:
"But we’re told there are 194 legs.
That’s 74 more than our guess."
Then write:
• "Reality: 194 legs"
• "Gap: 194 – 120 = 74"
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🔹 Step 4: Fill the gap.
Narrate:
"Each time we replace a chicken with a dog,
we gain 2 extra legs."
Then write:
• "+2 legs per dog"
• "74 ÷ 2 = 37 dogs"
Pause briefly.
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🔹 Step 5: Find the chickens.
Narrate:
"If 37 are dogs, then chickens = 60 – 37 = 23."
Then write:
• "Dogs = 37"
• "Chickens = 23"
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🔹 Step 6: Verify.
Narrate:
"Let’s double-check the math:
Dogs: 37 × 4 = 148
Chickens: 23 × 2 = 46
Total: 148 + 46 = 194 ✅"
Write each line after speaking.
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🔁 Step 7: Reverse assumption.
Narrate:
"What if we assume all are dogs?"
Then write:
• "All dogs → 60 × 4 = 240"
• "Overshoot: 240 – 194 = 46"
• "Each chicken saves 2 legs → 46 ÷ 2 = 23 chickens"
• "Dogs = 60 – 23 = 37 ✅"
Narrate:
"Same answer. Different direction."
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🔢 Step 8: Algebraic Method
Narrate:
"Let’s solve it a third way — algebra."
Then write:
• "Let x = number of dogs"
• "Then chickens = 60 – x"
• "Equation: 4x + 2(60 – x) = 194"
Narrate slowly and write step by step:
• "→ 4x + 120 – 2x = 194"
• "→ 2x = 74"
• "→ x = 37 dogs ✅"
• "→ Chickens = 60 – 37 = 23 ✅"
Narrate:
"Same truth. Modeled with algebra."
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🎯 Step 9: Key Insight
Narrate:
"The math hides a method."
Then write:
• "Gap ÷ Difference = Substitutions"
• "One idea. Three paths."
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🧩 Step 10: Bonus Challenge
Narrate:
"Before we wrap up — a challenge:
What if all 194 legs were dog legs?
How many heads are missing?
Or if all were chicken legs… how many extra heads did you imagine?"
Then write:
• "Bonus Q1: 194 legs → all dogs → heads?"
• "Bonus Q2: 194 legs → all chickens → heads?"
Prompt:
"If you solve either one — you’ve unlocked Hypothetical Thinking Level 2."
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🔁 Step 11: Strategy Migration
Narrate:
"This strategy goes beyond chickens and dogs."
Then write:
• "Mixtures → 'Assume all water?'"
• "Averages → 'Assume all perfect scores?'"
• "Work → 'Assume one person does the job?'"
Narrate:
"Assume. Adjust. Arrive."
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☁️ Step 12: Philosophy – Guessing = Flashlight
Narrate:
"Guessing isn’t a shortcut. It’s a flashlight.
It shows where logic breaks.
You don’t guess to skip — you guess to see."
Then write:
• "Guessing = Flashlight"
• "Assumptions aren't meant to be correct…
They’re meant to be correctable."
Then write:
• "One problem. Five paths. One truth."
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🎬 Step 13: Teaser for Next Episode
Narrate:
"Next time… we leave the farm.
And head to a ticket booth."
Then write:
• "50 tickets sold. $312 total."
• "Adults pay $8. Kids pay $4."
Narrate:
"Same strategy. Different world.
Hypothetical Reasoning — Strategy #02.
See you soon."
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📌 Engine Instructions:
Reveal one idea at a time.
Use whiteboard handwriting-style drawing.
Do not show all steps early.
Pause 2 seconds between concepts.
Narrate before writing each equation or insight.
视频信息
答案文本
视频字幕
You walk into a farm... Chickens clucking... dogs barking... Someone hands you this puzzle.
Let's assume every animal is a chicken. Even the ones... that clearly bark.
But we're told there are 194 legs. That's 74 more than our guess.
Each time we replace a chicken with a dog, we gain 2 extra legs.
If 37 are dogs, then chickens equals 60 minus 37 equals 23.
Let's double-check the math: Dogs: 37 times 4 equals 148. Chickens: 23 times 2 equals 46. Total: 148 plus 46 equals 194. Correct!
What if we assume all are dogs? All dogs would give us 60 times 4 equals 240 legs. That's an overshoot of 240 minus 194 equals 46 legs. Each chicken saves 2 legs compared to a dog, so 46 divided by 2 equals 23 chickens. That means we have 60 minus 23 equals 37 dogs. Same answer, different direction.
Let's solve it a third way — algebra. Let x equal the number of dogs. Then chickens equals 60 minus x. Our equation is: 4x plus 2 times 60 minus x equals 194. Simplifying: 4x plus 120 minus 2x equals 194. This gives us 2x equals 74, so x equals 37 dogs. And chickens equals 60 minus 37 equals 23. Same truth, modeled with algebra.
The math hides a method. Gap divided by Difference equals Substitutions. One idea. Three paths.
Before we wrap up — a challenge: What if all 194 legs were dog legs? How many heads are missing? Or if all were chicken legs… how many extra heads did you imagine? If you solve either one — you've unlocked Hypothetical Thinking Level 2.
This strategy goes beyond chickens and dogs. Mixtures, averages, work problems - all can use this approach. Assume. Adjust. Arrive.
Guessing isn't a shortcut. It's a flashlight. It shows where logic breaks. You don't guess to skip — you guess to see. Assumptions aren't meant to be correct… They're meant to be correctable. One problem. Five paths. One truth.