Question

Sam has a total of 7 coins. How many different ways will he arrange them in a row with the same number of coins?

• A. 1 × 7 and 7 × 1
• B. 3 × 4 and 4 × 3
• C. 2 × 5 and 5 × 2

Answer 1

The correct option is A 1 × 7 and 7 × 1

Sam has a total of 7 coins
7 is a prime number
Factors of 7 are 1 and 7 as follows
1 × 7
7 × 1
So, he could have arranged the coins in 1 row and 7 colums or 7 rows and 1 column

Let's C represents coins
Case 1:
1 Row 7 Columns: 1 × 7
C C C C C C C

Case 2:
7 Rows 1 Column: 7 × 1
C
C
C
C
C
C
C

3 Rows 4 Columns: 3 × 4
C C C C
C C
C

Each row does not contain the same number of coins. The first rows have 4 coins, while the last row has 1 coin.

4 Rows 3 Columns: 4 × 3
C C C
C C
C
C

Each row does not contain the same number of coins. The first row has 3 coins, while the last three rows have different number of coins.

Similarly, 2 rows and 5 columns (2 × 5) and 5 rows and 2 columns (5 × 2) are not possible.

Thus, the only possibility is that he could arrange the 7 coins into 7 × 1 dimensions or 1 × 7 dimensions