Is a well inflated tire less prone than a deflated tire to flatten due to a sharp object? When I bought my bike, I've been told that I should make sure the tires are well inflated because this reduces the risks of having a flat tire when rolling over sharp objects, and that it was easy to understand why. 
However, after almost a year later, I still haven't figured out why it would be the case, although I guess this is correct.
Here are my thoughts:


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*A well inflated inner tube can be considered as a torus with a greater volume than deflated inner tube. It also should have a reduced thickness, making it easier to pinch, I believe. An analogy would be an inflated balloon. If it's near exploding, its thickness surface is lesser than a deflated balloon, and I suppose it's also easier to pinch. I wonder why it wouldn't be the case for inner tubes of tires.

*According to several sources on the Internet (as well as one here), when one gets a flat tire, riding a bike becomes much harder due to increased rolling resistance. The usual reason given is that it takes a lot of energy to deform the tire, which is what happens while rolling with a flat tire. So a lot of energy spent with the legs is being used to deform the tire (and inner tube) rather than making the bike go forward. If that's true, then a sharp object should have a harder task to pinch a deflated tire than to pinch a well inflated tire. That's because a deflated tire would have to deform a lot before getting drilled by the sharp object, while the fully inflated tire wouldn't be able to deform much before getting drilled. So one would spend less energy to pinch a well inflated tire than to pinch a more deflated tire.
Thus, I am unable to find a good reason of how a well inflated tire would resist more to sharp pinching objects than a deflated tire. I'd appreciate if someone could point what I'm missing and how it counters the two points I made above.
As a sidenote, the optimal pressure of the inner tube of my bicycle is 2.5 bar to 4 bar. One can assume that by well inflated tire I meant 4 bar and by deflated tire I meant 2.5 bar. By flat tire I meant 1 bar (atmospheric pressure).
 A: Properly inflated the tire is harder and doesn't deform to grab the object (broken bottle, not precisely angled nail in a board; designed to defeat your tire and my answer).
With a 'ten speed bike tire' an improperly inflated tire would be wider, placing more surface in contact with the tiniest objects; like a small nail (or gyprock screw) lying flat on the road.
Overall I think the difference would be small (correctly inflated vs. slightly underinflated), no doubt it's best to properly inflate all varieties of tires in accordance with the manufacturer's direction (molded into the side of the tire).


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*A balloon is single layered, and some might argue, designed to pop. An inner tube is designed to operate properly and be safe for roadways when properly inflated and is protected from punctuation by the outer tire (made of harder rubber, since it is not inflated).

*When the tire is properly inflated you are riding on the outer edge of the torus (unless you have wide styled racing slicks, or solid tires like a forklift) but when it's not correctly inflated it's more akin to rolling dough with a rolling pin.
A: Comments to the post (v1):


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*Insufficient tire pressure leads to snakebites (pinch flats) for hopefully obvious reasons.

*Concerning OP's point 1: Inflating a balloon at (essentially) constant pressure cannot be compared with inflating a tire at (essentially) constant volume.
A: There are mainly two ways a tyre can flatten. By pinching and by piercing. Pinching won't occur if the tyre has the correct tension unless the wheel is overloaded. The probability of piercing increases with to the contact area, which is much smaller for a tyre at the right pressure.
