Class 6 NCERT bridge course Answers Activity W1.4 The “Guess My Number” Card Trick!

 Activity W1.4 

 Take two cards (paper or cardboard cutouts). 

Write some specific numbers from 1 to 4 on each of them. 

 Ask your friend to think of a number between 1 and 4; 

then, for each card, ask: "Is your number on this card?"; 

with their two yes/no answers, you should be able to tell them the number they thought of! 

 What numbers will you write on the two cards?

 Extension: 

There are six cards (which can be printed on one sheet of paper and then cut into six pieces) - each has numbers between 1 and 50; 

ask your friend/family member to think of a number between 1 and 50; 

shuffle the cards;

 then, for each card, ask: "Is your number on this card?"; 

with their six yes/no answers, you can tell them the number they thought of!

 How does it work?

Activity W1.4 – The “Guess My Number” Card Trick!

A Number Magic Using Logic and Cards!

Objective:

Use simple YES/NO questions with specially designed number cards to guess your friend’s secret number between 1 and 4 — or even up to 50!

Part 1: Guess a Number Between 1 and 4

 Step-by-Step:

1. Prepare 2 cards with the following numbers:

   • Card A: 1, 2

   • Card B: 2, 3

2. Ask your friend to secretly think of a number between 1 and 4.

3. Show each card and ask:
    “Is your number on this card?”

4. Based on the yes/no answers, you can guess the number!

Example:

• Friend thinks of: 2

• Card A? →  YES

• Card B? →  YES

• Only number common to both cards = 2

Why It Works:

You are narrowing down possibilities using logical elimination based on presence/absence in each card!

Extension: Guess Numbers Between 1 and 50

You can create 6 cards like this:

Each card contains numbers where a specific binary digit is 1 at certain positions. For example:

Card 1 (Bit 1 = 1)	1, 3, 5, 7, ..., 49
Card 2 (Bit 2 = 1)	2, 3, 6, 7, ..., 50
Card 3 (Bit 3 = 1)	4, 5, 6, 7, ..., 47
Card 4 (Bit 4 = 1)	8, 9, 10, 11, ..., 47
Card 5 (Bit 5 = 1)	16–31, 48–50
Card 6 (Bit 6 = 1)	32–50

How to Guess the Number:

1. Ask: “Is your number on this card?” for all 6.

2. For each YES, add the number associated with that card:

   • Card 1 = 1

   • Card 2 = 2

   • Card 3 = 4

   • Card 4 = 8

   • Card 5 = 16

   • Card 6 = 32

3. The sum of YES answers = Your friend’s number!

Example:

• Friend thinks of: 37

• Card 1? YES → +1

• Card 2? NO

• Card 3? NO

• Card 4? YES → +8

• Card 5? NO

• Card 6? YES → +32

Total = 1 + 8 + 32 =  41

Why It Works:

Each number between 1 and 50 can be represented as a binary number using 6 digits. Each card corresponds to one binary digit (bit), and their presence tells you which bits are "on."

Illustrative Image: “Guess My Number Cards”