<think>
Okay, let's see. I need to implement the rate_cap function. The goal is to raise a price by a whole-percent rate but not more than the stated largest increase. The new price should have the increase rounded down. If there's no increase, it just returns the original price.

First, I need to understand the parameters. The function takes price, rate, and most. The rate is a whole percent, so I guess it's an integer. The most is the maximum allowed increase. So, the increase is calculated as price * rate / 100, but that can't exceed most. But wait, the problem says to raise by a whole-percent rate, but cap it at most. So the actual increase is the minimum between (price * rate / 100) and most. But then, the new price is the original price plus this increase, but rounded down.

Wait, the problem says "return the new price, with the increase rounded down." So the increase is calculated as (price * rate) // 100? Or is it (price * rate) divided by 100, then floored? Or maybe the increase is (price * rate) // 100, but then if that's more than most, we cap it at most. Then add that to the original price.

Wait, the problem says "raise by a whole-percent rate, but never by more than a stated largest increase." So the increase is the minimum between (price * rate / 100) and most. But since we need to round down the increase, maybe the calculation is (price * rate) // 100, but then if that's more than most, we take most. Then add that to the original price.

Wait, but the problem says "the increase rounded down". So the increase is (price * rate) / 100, but rounded down. But if that's more than most, then we cap it at most. So the formula would be:

increase = min( (price * rate) // 100, most )

Then new_price = price + increase.

But wait, maybe the rate is a percentage, so for example, if price is 100 and rate is 10, then the increase is 10. If most is 5, then the increase is 5. So new price is 105.

But what if the rate is 15? Then (100 * 15) / 100 = 15, which is more than most (say 5). So the increase is 5, so new price is 105.

But how to calculate the increase? The problem says "the increase rounded down". So maybe the increase is (price * rate) // 100. But if that's more than most, then we take most. So the formula is:

increase = min( (price * rate) // 100, most )

But wait, what if (price * rate) is not divisible by 100? For example, price is 100, rate is 15. Then 100 * 15 = 1500, divided by 100 is 15. So that's exact. But if rate is 13, then 100 * 13 = 1300, divided by 100 is 13. So that's exact. But if rate is 13.5? Wait, but the rate is an integer. The problem says "whole-percent rate", so rate is an integer. So (price *