Daily Math Puzzle: 2026-10-02
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2026-10-02
You're at the electronics store buying several identical, rectangular boxes for your new home theater system. Each box measures 50 cm long, 30 cm wide, and 20 cm high. Your car's boot (trunk) has internal dimensions of 100 cm long, 75 cm wide, and 50 cm high. What is the maximum number of these boxes you can fit into your car's boot?
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Solution
10 boxes — To maximize the number of boxes, you must consider all possible orientations of the boxes within the boot. Let the boot dimensions be L=100cm, W=75cm, H=50cm, and the box dimensions be A=50cm, B=30cm, C=20cm.
We calculate the number of boxes that fit for each permutation of box dimensions mapped to boot dimensions:
1. **Box (A=50cm, B=30cm, C=20cm) aligned with Boot (L=100cm, W=75cm, H=50cm):**
* Along L: 100cm / 50cm = 2 boxes
* Along W: 75cm / 30cm = 2 boxes (2.5, so only 2 fit fully)
* Along H: 50cm / 20cm = 2 boxes (2.5, so only 2 fit fully)
* Total: 2 * 2 * 2 = **8 boxes**
2. **Box (A=50cm, C=20cm, B=30cm) aligned with Boot (L=100cm, W=75cm, H=50cm):**
* Along L: 100cm / 50cm = 2 boxes
* Along W: 75cm / 20cm = 3 boxes (3.75, so only 3 fit fully)
* Along H: 50cm / 30cm = 1 box (1.66, so only 1 fits fully)
* Total: 2 * 3 * 1 = **6 boxes**
3. **Box (B=30cm, A=50cm, C=20cm) aligned with Boot (L=100cm, W=75cm, H=50cm):**
* Along L: 100cm / 30cm = 3 boxes (3.33, so only 3 fit fully)
* Along W: 75cm / 50cm = 1 box (1.5, so only 1 fits fully)
* Along H: 50cm / 20cm = 2 boxes
* Total: 3 * 1 * 2 = **6 boxes**
4. **Box (B=30cm, C=20cm, A=50cm) aligned with Boot (L=100cm, W=75cm, H=50cm):**
* Along L: 100cm / 30cm = 3 boxes
* Along W: 75cm / 20cm = 3 boxes
* Along H: 50cm / 50cm = 1 box
* Total: 3 * 3 * 1 = **9 boxes**
5. **Box (C=20cm, A=50cm, B=30cm) aligned with Boot (L=100cm, W=75cm, H=50cm):**
* Along L: 100cm / 20cm = 5 boxes
* Along W: 75cm / 50cm = 1 box
* Along H: 50cm / 30cm = 1 box
* Total: 5 * 1 * 1 = **5 boxes**
6. **Box (C=20cm, B=30cm, A=50cm) aligned with Boot (L=100cm, W=75cm, H=50cm):**
* Along L: 100cm / 20cm = 5 boxes
* Along W: 75cm / 30cm = 2 boxes
* Along H: 50cm / 50cm = 1 box
* Total: 5 * 2 * 1 = **10 boxes**
The maximum number of boxes that can fit is 10. This occurs when the boxes are oriented with their 20cm side along the 100cm length of the boot, their 30cm side along the 75cm width, and their 50cm side along the 50cm height.
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