Ray makes an array that has 4 rows of 4 counters. He wants to make two more arreys using the same number of counters. He wants more than one counter in each row. What two arrays can he make?
Please help!
1 across and 16 down
To help Ray figure out what two arrays he can make, let's first consider the total number of counters he has. Ray starts with an array that has 4 rows of 4 counters, totaling 4 * 4 = 16 counters.
Now, since Ray wants to create two more arrays using the same number of counters, we need to divide the total number of counters (16) evenly among the three arrays.
To figure out the distribution of counters, we can consider the following conditions:
1. Each array should have more than one counter in each row, so we cannot have any rows with only one counter.
2. The number of counters in each array should be the same.
With these conditions in mind, let's find the possible configurations:
Option 1:
If we divide the 16 counters equally among the three arrays, each array would have approximately 16 / 3 = 5.33 counters. Since we cannot have a fraction of a counter, this option is not possible.
Option 2:
If we divide the 16 counters equally among the three arrays, but allow for one of the arrays to have fewer counters, we could distribute them as follows:
- Array 1: 6 counters (2 rows with 3 counters each)
- Array 2: 6 counters (2 rows with 3 counters each)
- Array 3: 4 counters (2 rows with 2 counters each)
Option 3:
If we cannot have any arrays with fewer counters, we need to consider distributing the counters unevenly among the three arrays. Let's explore this option:
- Array 1: 7 counters (2 rows with 3 counters each and 1 row with 1 counter)
- Array 2: 6 counters (2 rows with 3 counters each)
- Array 3: 3 counters (1 row with 3 counters)
Therefore, Ray can make two more arrays using the same number of counters with the following configurations:
Option 2:
- Array 1: 6 counters (2 rows with 3 counters each)
- Array 2: 6 counters (2 rows with 3 counters each)
- Array 3: 4 counters (2 rows with 2 counters each)
Option 3:
- Array 1: 7 counters (2 rows with 3 counters each and 1 row with 1 counter)
- Array 2: 6 counters (2 rows with 3 counters each)
- Array 3: 3 counters (1 row with 3 counters)
I hope this helps Ray with his task! Let me know if you have any further questions.