A Puzzle A Day: 2026-03-29

The Great Alakazam performs a wondrous act with his 'Shrinking Sphere'. When an object is placed inside, its volume magically halves every 10 seconds. If he places a special enchanted gem, how much total time from the moment it was placed in the sphere will it take for the gem to shrink to precisely 1/8th of its original volume?
Correct: 30 seconds
Let the original volume of the enchanted gem be V. The Shrinking Sphere halves the object's *current* volume every 10 seconds. This is an exponential rate of change. 1. **After the first 10 seconds:** The volume becomes V / 2. 2. **After another 10 seconds (total 20 seconds):** The gem's *current* volume is V/2. Halving this current volume means it becomes (V / 2) / 2 = V / 4. 3. **After yet another 10 seconds (total 30 seconds):** The gem's *current* volume is V/4. Halving this current volume means it becomes (V / 4) / 2 = V / 8. Therefore, it takes a total of 30 seconds for the gem to shrink to precisely 1/8th of its original volume.
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