# Some things are best said in plain language instead of mathematical notation!

Back then in 2013 when I was participating in International Olympiad in Informatics (IOI), I was stumbled on the puzzles on their newsletters. Even until now, I'm pretty clueless for these.

Here are two of them. Could you help me to crack it?

• You may have better luck on the Mathematics page if you find that us puzzlers can't solve it :) Aug 16, 2018 at 12:33
• Adding to what @elarr commented above, I strongly recommend you post this on the Mathematics Stack Exchange (Math SE). Aug 16, 2018 at 12:36
• @elarr Don't write us off just yet, we might be on to something :D Aug 16, 2018 at 13:43

I think this can be solved without math knowledge:

("Empodia", 2004) is

the name of the 4th task of the 2004 IOI

so the solution is probably

the 4th task of some other IOI?

Edit:

I think the second solution could be

("Buses", 2008) - the "Buses" task of the 2008 IOI, since the task description matches the mathematical notation... I think. Here is the link to that year's tasks: IOI2008

• I was just about to comment this! (+1) :D I wasn't sure though, because this puzzle is only related to Empodia by name; the actual task for Empodia that year didn't appear to have anything to do with the mathematical notation that is associated to it here... Aug 16, 2018 at 12:44
• @El-Guest Yeah, I just realized that too :D I'm guessing the notation is equivalent to the written task, in which case we do need mathematical knowledge (big time) to solve this... Aug 16, 2018 at 12:47
• Eutherpy, I think you're more correct than I am...the more I look at Empodia, the more that I'm starting to see similarities between that task and this notation. Aug 16, 2018 at 12:52
• Aah, I see now.. So all of those mathematical notations describe past IOI problems (and we need to find it), and indeed the task description - in plain language - is preferred to be read rather than the notations! Thanks a lot!! :D. Btw I'm accepting this answer as it's the first that hinted the way to solve the puzzle. Also +1 for @ffao's answer for the second puzzle. Aug 17, 2018 at 0:40

("Pairs", 2007)

Because the math states:

Given the dimensionality of the board $a = B$, a max distance $b = D$, and a set of animals $C$, how many pairs of animals can hear each other (that is, what is the size of the set of pairs of animals such that their distance is at most $b$)?

• I think I sort of get what the first one says, but I don't know enough IOI problems to know what they framed it as...
– ffao
Aug 16, 2018 at 19:57
• The one from Croatia, yes! I stumbled upon that one and it caught my eye, but I wasn't sure and decided not to answer :) Aug 16, 2018 at 21:35

To add my two cents to @Eutherpy's answer, in plain language it appears that

given an integer $k$ and an invertible (apparently on $\mathbb{Z}$) function that maps the large interval $[1,k]$ to itself, we're trying to find the biggest set of intervals where (a) no element appears in more than one interval in the set, and (b) when you apply the function $\pi$ to any element in any interval, the interval remains the same size but shifts up.

An example for k = 5 (not the correct solution) seems to be:

using the function $\pi(x) = x+1$, where if we assume $a<b$ as is common for intervals, we could have the set $\{ [1,2] , [3,4] \}$ be maximal. Facetiously, since there is no $a<b$ restrictiion, the maximal solution would be $\{[1,1] , [2,2], [3,3], [4,4] \}$...but I have no idea on how that relates to the framed intervals from the Empodia problem.