Basic Math

Logical reasoning | Second Grade

🧩 Logical Reasoning - Guess the Number

What is "Guess the Number"?

"Guess the Number" is a logical reasoning game where you use clues to find a mystery number!

You read the clues carefully, think logically, and eliminate wrong answers until you find the correct number.

🔍 Types of Number Clues

1️⃣ Comparison Clues (Greater Than / Less Than)

These clues tell you if the mystery number is bigger or smaller than another number.

Important Symbols:

  • • \(>\) means "greater than" (bigger)
  • • \(<\) means "less than" (smaller)
  • • \(=\) means "equal to" (same)

Examples:

Clue: "The number is greater than \(5\)"
Meaning: Number \(> 5\)
Possible numbers: \(6, 7, 8, 9, 10...\)

Clue: "The number is less than \(8\)"
Meaning: Number \(< 8\)
Possible numbers: \(1, 2, 3, 4, 5, 6, 7\)

2️⃣ Between Clues

These clues tell you the mystery number is between two numbers.

Formula:

If number is between \(a\) and \(b\), then:
\(a < \text{number} < b\)

Example:

Clue: "The number is between \(10\) and \(15\)"
Meaning: \(10 < \text{number} < 15\)
Possible numbers: \(11, 12, 13, 14\)
Note: We do NOT include \(10\) or \(15\)!

3️⃣ Even and Odd Number Clues

These clues tell you if the mystery number is even or odd.

What are Even Numbers?

  • Even numbers end in \(0, 2, 4, 6,\) or \(8\)
  • They can be divided by \(2\) with no remainder
  • Examples: \(2, 4, 6, 8, 10, 12, 14, 16, 18, 20...\)

What are Odd Numbers?

  • Odd numbers end in \(1, 3, 5, 7,\) or \(9\)
  • They cannot be divided by \(2\) evenly
  • Examples: \(1, 3, 5, 7, 9, 11, 13, 15, 17, 19...\)

Formula:

Even Number: \(2n\) (where \(n = 1, 2, 3...\))
Odd Number: \(2n - 1\) or \(2n + 1\)

4️⃣ Place Value Clues

These clues tell you about specific digits in the ones, tens, or hundreds places.

Place Value Chart:

HundredsTensOnes
\(2\)\(4\)\(7\)
\(200\)\(40\)\(7\)

The number is \(247\)

Example:

Clues:
• The digit in the tens place is \(3\)
• The digit in the ones place is \(5\)
Answer: The number could be \(35, 135, 235, 335...\)
(More clues needed to find the exact number!)

5️⃣ Sum of Digits Clues

These clues tell you what all the digits add up to when added together.

Formula:

Sum of Digits = Digit₁ + Digit₂ + Digit₃ + ...

Example:

Clue: "The sum of the digits is \(12\)"
For number \(48\): \(4 + 8 = 12\) ✓ (This could be the answer!)
For number \(57\): \(5 + 7 = 12\) ✓ (This could also work!)
For number \(66\): \(6 + 6 = 12\) ✓ (Another possibility!)
For number \(75\): \(7 + 5 = 12\) ✓ (Yes, this too!)

🎯 Problem-Solving Strategies

Strategy 1: Elimination Method

Cross out numbers that don't match the clues!

  1. Read the first clue carefully
  2. Cross out all numbers that don't match
  3. Read the second clue
  4. Cross out more numbers that don't match
  5. Keep going until only one number is left!

Strategy 2: Narrowing Down

Use each clue to make the range smaller!

Step 1: Start with all possible numbers: \(1-20\)
Step 2: Clue says "greater than \(10\)": now \(11-20\)
Step 3: Next clue says "less than \(16\)": now \(11-15\)
Step 4: Next clue says "even number": now \(12, 14\)
Step 5: Last clue says "digits add to \(6\)": Answer is \(15\)? No! It's odd.
Wait! \(1 + 2 = 3\) and \(1 + 4 = 5\)... need to reconsider!

Strategy 3: Guess and Check

Make smart guesses and test them!

  1. Pick a number in the middle of the range
  2. Check if it matches ALL the clues
  3. If it's too big, try a smaller number
  4. If it's too small, try a bigger number
  5. Keep checking until you find the answer!

📖 Complete Worked Examples

Example 1: Using Comparison Clues

Problem:

Guess the number between \(1\) and \(10\):
• The number is greater than \(5\)
• The number is less than \(9\)
• The number is even

Solution:

Step 1: Greater than \(5\) means: \(6, 7, 8, 9, 10\)
Step 2: Less than \(9\) means: \(6, 7, 8\)
Step 3: Even numbers only: \(6, 8\)
Wait! We need more clues or both could be correct!
If we add: "The digits add to \(8\)" → Answer is \(8\) because \(8 = 8\)

Example 2: Using Place Value Clues

Problem:

I'm thinking of a 2-digit number:
• The digit in the tens place is \(4\)
• The digit in the ones place is \(7\)
What is the number?

Solution:

Tens place: \(4\) → This means \(40\)
Ones place: \(7\) → This means \(7\)
Total: \(40 + 7 = 47\)
Answer: The number is \(47\)! ✓

Example 3: Using Sum of Digits

Problem:

Jane is thinking of a 3-digit number:
• All three digits are the same
• The sum of the digits is \(12\)
What is the number?

Solution:

Method 1 (Addition):
All digits are the same, so: \(\text{digit} + \text{digit} + \text{digit} = 12\)
Try: \(1 + 1 + 1 = 3\) ✗
Try: \(2 + 2 + 2 = 6\) ✗
Try: \(3 + 3 + 3 = 9\) ✗
Try: \(4 + 4 + 4 = 12\) ✓
Answer: \(444\)

Method 2 (Multiplication):
\(\text{digit} \times 3 = 12\)
\(\text{digit} = 12 \div 3 = 4\)
Answer: \(444\)

📋 Step-by-Step Guide to Solve Any "Guess the Number" Problem

  1. Read ALL the clues carefully before starting
  2. Understand what each clue means (greater than, less than, even, odd, etc.)
  3. List all possible numbers from the range given
  4. Use the first clue to eliminate numbers that don't work
  5. Apply each clue one by one and keep crossing out wrong answers
  6. Check your answer against ALL clues to make sure it works
  7. Write your final answer clearly!

⚠️ Important Reminders

  • ✓ Read each clue carefully and slowly
  • ✓ Don't skip any clues - they ALL matter!
  • ✓ Check if your answer works with EVERY clue
  • ✓ If you get multiple answers, you need more clues
  • ✓ Show your work step by step
  • ✓ Double-check before writing your final answer

📊 Quick Reference Chart

Clue TypeWhat It MeansExample
Greater than \(>\)Number is bigger\(> 5\) means \(6, 7, 8...\)
Less than \(<\)Number is smaller\(< 8\) means \(7, 6, 5...\)
BetweenNumber is in the middleBetween \(5\) and \(10\) means \(6, 7, 8, 9\)
EvenEnds in \(0, 2, 4, 6, 8\)\(2, 4, 6, 8, 10, 12...\)
OddEnds in \(1, 3, 5, 7, 9\)\(1, 3, 5, 7, 9, 11...\)
Place ValueSpecific digit in a placeTens digit is \(3\) → \(30, 31, 32...\)
Sum of DigitsAll digits add up to...Sum = \(10\) → \(19\) because \(1 + 9 = 10\)

📝 Important Formulas & Rules

Comparison Symbols:

\(a > b\) → \(a\) is greater than \(b\)
\(a < b\) → \(a\) is less than \(b\)
\(a = b\) → \(a\) equals \(b\)

Even and Odd Rules:

Even Number: \(2n\) where \(n = 1, 2, 3, 4...\)
Odd Number: \(2n - 1\) or \(2n + 1\)
Even + Even = Even
Odd + Odd = Even
Even + Odd = Odd

Place Value Formula:

\(\text{Number} = (\text{Hundreds} \times 100) + (\text{Tens} \times 10) + \text{Ones}\)

Example: \(347 = (3 \times 100) + (4 \times 10) + 7\)
\(= 300 + 40 + 7\)

Sum of Digits Formula:

For a 2-digit number \(AB\):
Sum = \(A + B\)

For a 3-digit number \(ABC\):
Sum = \(A + B + C\)

💡 Practice Tips for Success

  • Read slowly: Don't rush through the clues!
  • Underline key words: "greater than", "even", "sum", etc.
  • Write down possibilities: List all numbers that could work
  • Cross out wrong answers: Use elimination method
  • Check ALL clues: Your answer must match every single clue
  • Use scratch paper: Show all your thinking and work
  • Practice daily: The more you practice, the faster you'll get!
  • Think logically: Use your brain like a detective! 🔍
  • Don't give up: If one strategy doesn't work, try another!
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