The elk puzzles

[theelkspeaks]

From time to time, I thought it would be fun to share some little puzzles with the Elements Community!  These will generally be short questions or riddles, and I'll give some "points" dependent on the difficulty of the puzzle to the first person to give a correct answer in this thread! I'll keep a leaderboard in the OP.  Good luck to all!

The third puzzle will be live: now.

1. Linkcat - 3 points
2. ddevans96 - 2 points

[theelkspeaks]

(2 points) Give the next THREE numbers in the following sequence (/ used to represent fractions): 1, 2/3, 1/2, 2/5, 1/3, ....

Reminder: the first correct answer in this thread gets the points! Good luck!

[Linkcat]

2/7, 1/4, 2/9

[theelkspeaks]

Very good!

Solution: The sequence is the fraction of dots in a triangle in the bottom row of that triangle.

So for a 1 row triangle, it's all of the dots.  For a 2 row triangle, it's 2/3 dots, for 3 rows, 3/6 which is 1/2, and so on!

[theelkspeaks]

Congratulations Linkcat!


The second puzzle will be live: now.

Leaderboard

1. Linkcat - 2 points!

[Linkcat]

Seems like a good spot to end the thread, elk.

[dragtom]

I like the idea of this thread, but it looks like very often the question will be answered before people have a chance to look at it.
perhaps have a time when you reveal the answer, and have people give 1 answer in spoilers.
Only the 1st post with the right answer (and maybe also explanation?) gets the points.

[Submachine]

I like the idea of having a thread where simple logic puzzles can be posted. I used to post them in the Guilds Puzzle thread, but that would be outdated today.

[theelkspeaks]

These are more intended to be individual puzzles than guild puzzles anyway, so regardless of the status of guilds, it doesn't quite fit there - hope to see you join in!

[Captain Scibra]

I was going to say the pattern is more easily understood as 2/(n+1), which actually is actually what the pattern you described simplifies into.  Because the number of dots of a triangle can be derived using the number of dots on one of the sides (technically doesn't matter which one), the patter you described cancels out the base incorporation of said number (n) and leaves you with the inverse of the extension.

[theelkspeaks]

(2 points) Eight runners are having a race.  They are in lanes 1-8.  Please order the lane numbers from fastest to slowest runner.

You know the following pieces of information:

1.   The runner in lane 7 finishes directly after the runner in lane 1.
2.   The runner in lane 5 is slower than the runner in lane 3.
3.   The runner in lane 6 finishes outside the top 3.
4.   The runner in lane 2 defeats the runner in lane 5, but loses to the runner in lane 4.
5.   Of the top 3 runners, the runner with the lowest lane number finishes in 3rd place.
6.   The runner in lane 3 is faster than the runner in lane 8.
7.   The runner in lane 4 finishes directly before the runner in lane 6.
8.   The three fastest runners’ lane numbers have a sum of 12.

[Linkcat]

3
8
1
7
6
4
2
5