Final answer:
Carrie can make her collage using 36 tacks by arranging the 16 snapshots in a 4x4 grid. This allows for the most efficient use of tacks since one tack can fasten up to 4 corners in the center, 2 on the edges, and each corner snapshot needs only one tack.
Step-by-step explanation:
Carrie intends to create a collage on a cork-board using 16 snapshots. To secure each snapshot using the least number of tacks, we need to determine the most efficient way of placing the snapshots. We can assume that each snapshot is a square with four corners.
If she places the pictures in a grid pattern without overlapping, the most corners that can meet at one point is four (from four different snapshots). Hence, one tack can secure the corners of up to four different snapshots.
Let's arrange the snapshots in a 4x4 grid. The four corners in the center will be shared by 4 snapshots, reducing the number of tacks at these points. For the outer edges, each tack can secure the corner of 2 snapshots (except the four corners of the grid which are shared by 1 snapshot)
Calculation:
- For the center: 1 tack for each of the four points where four snapshots meet.
- For the edges: Half of the remaining points are on the edge where each requires 1 tack for every 2 snapshots.
- For the corners: 4 tacks for the four corners of the grid where only one snapshot is present.
The total number of tracks needed is calculated as:
- 4 tacks for center points
- + (16 snapshots x 4 corners - 4 center points - 4 corner points) / 2 (since each tack can hold 2 corners)
- + 4 corner tacks
That gives us 4 + (64 - 4 - 4) / 2 + 4 = 36 tacks