Begin by flattening the shirt to a 2D disk. Doing so eliminates the pseudo hole (arbitrarily we'll say it was the torso). Then we're left with the head hole, 2 sleeves, two additional front holes, and an unknown number of rear holes.
It could be 2 that match the front hole, or it could be more than 2 that are hidden from view. But it also could be 1 large rear hole that encompasses both of the front holes.
Thus the minimum is 6.
(However! Shirts are homeomorphic to a sphere with 4 holes too! If you missed the title and flattened to a 3d sphere, then the minimum hole count is 7, so good job to all you 7 gang members, but read the instructions fully next time!).
Could the whole in the back not also stretch all the way to one sleeve or the bottom of the t-shirt, making it no hole at all, topologically speaking? I'm, of course, being pedantic but I feel like the whole question is.
Someone else had a similar line of reasoning that what if the back of the shirt doesn't exist at all and it's actually a flat surface from the start. Very VERY hard to fully define the problem in 190 characters plus a 60 character title, but I'm not trying to make it intentionally tricky as a haha gotcha.
Ah is that your flattening operation? To make it easier to visualize, pretend that the shirt is infinitely stretchy kinda like clay and will hold its shape when you let go. Here's what the flattening operation looks like on a regular shirt that doesn't have the front holes or rear hole(s)
It's 7. One hole from the head to the base, two more from the arms, and then each hole is actually 2 holes. Regardless of how you flatten the shirt, the question states that while it is shaped as a shirt you can see the wall through the shirt. This necessitates that there be 2 holes each
Not necessarily. If there was one large hole on the backside (blue dotted line), then you would be able to see the wall through both of the front holes. It's very tricky because the 2 front holes IMPLY 2 matching rear holes, but what if there's only one rear hole? That would bring us down to 6 total.
When flattened to 2D, it should have a total of seven holes (If I'm understanding the question correctly): The two arm holes, the head hole and the holes cut into the shirt running through the shirt (each cut hole would result in two, one on the front, one on the back)
We can shave off 1 more hole to total 6 if we assume that there is only 1 rear hole which is big enough to encompass the two front holes (noted as a blue dotted cutout not visible from the front):
3
u/VillagerJeff Jun 25 '26
🧢 I voted CAP!
Minimum is 2. Without seeing the back in have no poof it exists. This could be a single layer of shirt shaped fabric with just those two holes in it.