Puzzle time - the ant lottery
-
Well you get to see them all.
And you have this one tool.
The ant lottery sub-plot is just there to improve the ratings.
@jon-nyc said in Puzzle time - the ant lottery:
Well you get to see them all.
In other words you can’t choose a number you didn’t see. Then the problem would be trivial.
-
@jon-nyc said in Puzzle time - the ant lottery:
Well you get to see them all.
In other words you can’t choose a number you didn’t see. Then the problem would be trivial.
@jon-nyc said in Puzzle time - the ant lottery:
@jon-nyc said in Puzzle time - the ant lottery:
Well you get to see them all.
In other words you can’t choose a number you didn’t see. Then the problem would be trivial.
What does “maybe too many for you to record” from the original statement mean?
Education is extremely important.
-
-
I think it’s ruling out the idea that you capture the highest number and run it through your random number generator until it selects a participating ant.
@jon-nyc said in Puzzle time - the ant lottery:
I think it’s ruling out the idea that you capture the highest number and run it through your random number generator until it selects a participating ant.
But how would you know when to stop, that is, when you’ve hit a number that occurred on a tag? You mean when you have the full list, right?
-
@jon-nyc said in Puzzle time - the ant lottery:
@jon-nyc said in Puzzle time - the ant lottery:
Well you get to see them all.
In other words you can’t choose a number you didn’t see. Then the problem would be trivial.
What does “maybe too many for you to record” from the original statement mean?
@horace said in Puzzle time - the ant lottery:
@jon-nyc said in Puzzle time - the ant lottery:
@jon-nyc said in Puzzle time - the ant lottery:
Well you get to see them all.
In other words you can’t choose a number you didn’t see. Then the problem would be trivial.
What does “maybe too many for you to record” from the original statement mean?
If there’s a fixed space limit - say, 1000 digits- then one may not even be able to write down a single Identifier. They could all be bigger than the limit.
The nature of that limit seems pretty vague. Is it a fixed number of identifiers? A fixed number of digits? Is its size predetermined or can I choose the size? Or is the only purpose of that statement to rule out the "record every identifier" strategy and otherwise there are no limits? I assume it is the latter.
-
:::
The simple case for one ant is that the first ant has a 100% chance of winning. The case for two ants is that you roll a 50/50 shot for whether that new ant wins, and if not the current winner wins. This leaves a 50/50 shot for each ant. Third ant, you roll a 1/3 shot for it to win, if not then the current winner stands. Those two first ants each had a .5 chance to be the current winner, and now that the third ant might be the winner, they have a .5 * 2/3 chance, or 1/3, just like the third ant. Fourth ant comes along, it is given a 1/4 chance of winning, and if it doesn't, the current winner stands, who had a 1/3 * 3/4 chance of being winner, or 1/4. And so on...
:::
-
Yep.
:::
I worked backwards from the last ant. She needs a 1/n chance. Second to last would have had her 1/(n-1) chance followed by a (n-1)/n chance. From there I generalized to ant k and saw that the pattern holds.
:::
-
Yep.
:::
I worked backwards from the last ant. She needs a 1/n chance. Second to last would have had her 1/(n-1) chance followed by a (n-1)/n chance. From there I generalized to ant k and saw that the pattern holds.
:::
@jon-nyc said in Puzzle time - the ant lottery:
Yep.
:::
I worked backwards from the last ant. She needs a 1/n chance. Second to last would have had her 1/(n-1) chance followed by a (n-1)/n chance. From there I generalized to ant k and saw that the pattern holds.
:::
When the puzzle author found themselves with a trivially solvable problem scenario and had to add that kludge about not being able to record all the ant IDs, that's when they should have re-thought the whole scenario and found a better one that didn't have a trivial solution.
-
Horace's solution makes sense, but I also think the description is confusing and overly complicated.
@klaus said in Puzzle time - the ant lottery:
Horace's solution makes sense, but I also think the description is confusing and overly complicated.
How about the objective is to take a picture of the winning ant, but your digital camera has storage for only one picture, which can be overwritten any number of times with a new photo.
-
@klaus said in Puzzle time - the ant lottery:
Nice idea!
Thanks Klaus. Another problem with not being able to record the ID of every ant is that the solution assumes a non zero chance of having to record every ant, as the interim lottery winner.
