| Lingyis said: i didn't check if 57 and 7 would work if you round down any fractional number... but i'd say that if the original problem didn't say you can round up or down, you probably would be better off sticking with natural numbers. especially since there is a solution that works! but 57 & 7 would be a cool extension to the problem. with regards to your equation, i don't think the problem implied that the same number of medals were given out each day, so i don't think you can quite make that assumption. here's why the last day has to be a multiple of 6 because of the 1/7 condition--it's really obvious once you see it. since on the previous day 1/7 of the the rest of the medals were given out, that means there are 6/7 of medals left for the next day. now, on the last day, you give away all the remaining medals, which has to be 6/7 of some integer. now you see why that last day has to be a multiple of 6! once you realize that the number of days n = 6*i where i is some integer, of course you proceed to test if i=1 works. turns out it does, and gives a very nice, symmetric solution (6 medals a day for 6 days), so you can bet your money that it's the right answer. however, you still need to show that it's the only solution. this part isn't that hard although it's a little tricky, but essentially you show that only when i=1 you can ensure you get integer value of medals awarded on every single day. |
It doesn't, in fact, in the beginning I considered k to be different each time (k1, k2, etc.), where all k are integer numbers, and the only thing that matters is the absolute value (for example, my answer was not 12 in the other try, it was -12; but I only had to consider the absolute value for it to work).
Then I thought that maybe k1= k2 is one solution and proceeded to do the exercise that way, and it worked, giving answers 36 and 6.
For when k1/=/k2, the answer would be 57 and 7, but of course the value of the 1/7 part of the addition is not an integer all times. Then you have to lower to the highest natural number before it for it to work. If you're not allowed to do that, k won't be an integer, and since it must be an integer, then the only answer is 36 and 6.
I understand what you mean about 6 being a multiple of the answer, but keep in mind that you're not giving away 1/7 each day, you're giving away 1/7 +1, 1/7+2, 1/7+3.
In any case, we got the answer right congrats!
I'll post a problem later, though it'll probably be a little easier. Well, if you know geometry that is. Umm...this is an embarrasing question...what's the button combination for printing the screen?
