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And can this be expressed somehow using v?

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We need a mathematical expression for the spider's speed module, at which it can catch an ant.

As Ment explained: v/sqrt(3) + o(v) – this is the speed the spider should have – for any arbitrarily small value greater than the ant's speed divided by the square root of three. Then it will be able to catch it.

the spider's speed is any value, however small, greater than the ant's speed divided by the square root of three. Then it will be able to catch it.

Hmm... May I ask where this "problem" came from?

I saw it on another forum, but I don't remember exactly how it was described there. At first, I, like Ment, thought that the spider should intercept it perpendicularly, but then one guy proved that for an equilateral triangle, if it intercepts it at a 60-degree angle, it will be faster. I then built a dependency of the ratio of the distance traveled by the spider to the distance traveled by the ant on the angle, found its derivative, and realized that yes, it will be minimal when the spider runs at an angle of 60 degrees to intercept the ant, and not at a right angle (and for the triangle, the speed will be greater than v/2). And for a regular tetrahedron, since its edges are inclined at an angle of arccos(1/3^1/2), the path that the spider must travel must be multiplied not by cos 60, as in the triangle, but by cos(arccos(1/3^1/2)), that is, the spider's speed should be as Ment said.

Okay, I understand. The question is simply phrased incorrectly. v/sqrt(3) is not sufficient (it won't catch up), and v/sqrt(3) + "a little bit" is too much, because at a speed of v/sqrt(3) + "a little bit"/2, the ant will also be caught. But v/sqrt(3) + "a little bit"/2 is also incorrect, as v/sqrt(3) + "a little bit"/4 is also sufficient to catch it. In short, it's like asking for the smallest number in the interval (0;1), for example... The correct answer is: "Such a speed does not exist". :D

I thought about this before writing, which is why I phrased the question not as "what should it equal," but as "what should it be." And the mathematical expression, as I put it then, doesn't necessarily imply equality – it could also be an inequality. Well, maybe my terminology isn't quite right.

Jesus fed 5,000 people with five loaves of bread. Calculate how many kilojoules of energy one person received, knowing that the weight of one loaf was 1.5 kg, and the energy value of the bread is 800 kJ/100g?

12

Well, since no one wants to propose a riddle, I'll try to come up with one to revive the topic. I had a great idea for a riddle about springs, a weight, and a tin can, but I need to think it through, so for now, here's this riddle.

How many times a day do the hour and minute hands form an angle of 120^o? The riddle must be solved without moving the clock hands and without observing the clock for an entire day.

48?

No.

and without monitoring the clocks for 24 hours.

:(

Why not? The hour hand has 24 static positions in a day. The minute hand forms a 120-degree angle with it once in the first half of the hour and once in the second half of the hour. That is, twice an hour. 2 x 24 = 48.

It seems there's a catch here: while the minute hand covers those 20 or 40 minutes, the hour hand will also move. So, we'll have to calculate it a bit more complexly. Achilles and the tortoise – will he catch up or not?

These are some rather peculiar watches.