Question

A cube has its six faces numbered 1 to 6. A school boy tosses up the cube twice and notes down the two numbers appearing on top in these two tosses. He multiplies these two numbers and notes down the result. How many unique multiplication results can he possibly get through this tossing game?

Hint:

When counting products, always reduce duplicates (e.g., $2\times3$ and $3\times2$ are the same).

Answer 1

Step 1: Possible numbers.
Faces are numbered 1 to 6.
Step 2: Possible products.
All products $i \times j$ where $i, j \in \{1,2,3,4,5,6\}$.
Step 3: Compute unique values.
Products:
- With 1: {1,2,3,4,5,6}
- With 2: {2,4,6,8,10,12}
- With 3: {3,6,9,12,15,18}
- With 4: {4,8,12,16,20,24}
- With 5: {5,10,15,20,25,30}
- With 6: {6,12,18,24,30,36}
Unique products = {1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,30,36}.
Step 4: Count.
Total unique values = 18.
Final Answer: \[ \boxed{18} \]