Your Name - Ishika Jain
Your School Name - St Mary’s School
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Problem - Understand the Idea of How can we represent any number using only two symbols (0 and 1)?
Solution -
To understand the concept we created a GAME where we listed down 31 dishes across 5 columns (A,B,C,D,E). And then each dish was also given a unique number in a separate sheet. And this sheet is what is being shown to the user and is asked to select one dish about out of it. And do not share the name.
Then the user is asked in which all columns the dish appear and based on the selected columns the name of the dish is told.
Using Binary Number System Every number from 1 to 31 can be written as:
N=b0(20)+b1(21)+b2(22)+b3(23)+b4(24)
Where each bi is either:
-
0 (not selected)
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1 (selected)
Since:
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2^0 = 1
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2^1 = 2
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2^2 = 4
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2^3 = 8
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2^4 = 16
Maximum number: 1+2+4+8+16=31 , So any number between 1 and 31 can be formed
Game Structure (How It Works):
create:
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31 dishes
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Number them secretly from 1 to 31
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Prepare 5 columns (A, B, C, D, E)
Each column represents a power of 2:
| Column | Value | Power |
|---|---|---|
| A | 1 | 2⁰ |
| B | 2 | 2¹ |
| C | 4 | 2² |
| D | 8 | 2³ |
| E | 16 | 2⁴ |
How to Arrange the Dishes
For each dish number:
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Convert the number into binary
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Place that dish in all columns where binary digit = 1
Example:
Dish number 6
6 in binary = 00110
That means:
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2² (4) → yes
-
2¹ (2) → yes
So it appears in:
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Column B (2)
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Column C (4)
When player says: “My dish is in B and C”
We calculate: 2+4=62 + 4 = 62+4=6
Dish number = 6
