Question: A historian of astronomy arranges 4 identical celestial maps and 3 distinct telescopes on a shelf. How many distinct arrangements are there?

Sun, 03 May 2026 14:43:22 +0000

**Discover Hook: Why the Arrangement of Celestial Maps and Telescopes Holds Surprising Math in Astronomy History**
A historian studying the past often encounters physical exhibits—artifact displays where celestial maps rest beside instruments like telescopes, each placed with purpose. When presented with a shelf featuring four identical celestial maps and three distinct telescopes, a deceptively simple question arises: *How many distinct arrangements are possible?* This isn’t just a niche puzzle—it reflects deeper patterns in categorization, symmetry, and historical inventory, keywords now trending among science enthusiasts, educators, and students exploring STEM through tangible history. For mobile users seeking clarity over chaos, this question taps into the growing interest in accessible, meaningful data—a sign of broader digital curiosity about science’s cross-disciplinary storytelling. **Why This Question Matters in Understanding Historical Arrangements**
In museum curation and academic display, arranging physical items involves more than aesthetics—each placement tells a story. When collectors or historians face identical artifacts and unique instruments, even small variations in layout reflect intentional design choices. The real-world setup of four identical celestial maps and three distinct telescopes forces a precise count: how many unique orders can exist when repetition limits one type but variation enhances it. Answers to such spatial puzzles inform better cataloging, exhibit design, and educational framing—particularly relevant as digital archives increasingly prioritize meticulous classification. For US-based learners and cultural observers, this problem bridges everyday curiosity and advanced pattern recognition, grounded in real historical practices. **How Many Distinct Arrangements Are There? The Breakdown**
At first glance, the shelf holds seven items: four identical celestial maps and three distinct telescopes. Because the celestial maps are indistinguishable, swapping one map with another produces no new arrangement. However, each telescope is unique, so their placement matters deeply. This distinction defines the mathematical core: the problem reduces to placing the three distinct telescopes among the seven positions while the maps fill the rest—no two arrangements where identical maps occupy spots are counted twice, but every telescope placement contributes uniquely. Mathematically, the solution begins by choosing three positions out of seven for the telescopes. The number of ways to select three slots from seven is given by the combination formula:
**C(7, 3) = 7! / (