New answers tagged optimization
1
vote
Irregularly Deposited Compound Interest
My own solution
The following is the solution I had when I posted this puzzle. It loses to Albert.Lang's answer, but beats others.
First observation:
Second observation:
Third observation:
That ...
- 2,434
1
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Irregularly Deposited Compound Interest
Consider an interval, over which a newly-deposited balance of $b$ accrues an interest amount $i$.
Why?
Let's crunch some numbers!
And now, a simple program: invest(balance, interest rate, time) ...
- 8,194
4
votes
Accepted
Irregularly Deposited Compound Interest
Observation: Let's for the moment assume we know the optimal number of transfers and need only optimise the timing. Freezing all but one transfer (#k, say) we find that its best timing $t_k$ only ...
- 3,991
3
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Irregularly Deposited Compound Interest
Not sure if I'm right here, but this is my best solution.
First of all, in my solution:
So, with that, I came up with the following formula:
Since I wasn't able to think of a way to expand that ...
- 634
8
votes
Three 8-letter words with at least 23 different letters
Looking for three 8-letter word groups with 24 distinct letters.
I was unable to find a solution in a dictionary, but did find several by using other word lists. Most are 'suspect' but this one uses ...
- 13.7k
3
votes
Crossing desert with smallest amount of water
This puzzle is similar to the standard desert crossing puzzle, except that after you cross over, you then need to return to the origin. Because of this difference, you can leave water caches to be ...
- 17.8k
20
votes
Accepted
Three 8-letter words with at least 23 different letters
Searching a list of over 8000 eight-letter words with no repeated letters yields the following six triples, each with 23 distinct letters:
- 13.4k
2
votes
Accepted
2
votes
Dissecting a square
A near miss for $D=5$ and $N=7$, with $12$ polyominoes and largest area $8$ instead of $\le 7$:
The underlying $5$-regular connected planar graph is the icosahedral graph.
- 11.9k
16
votes
Accepted
Minimum number of turns
Oo, I've got this one; these come up a lot while organising board game tournaments.
a) what is the minimum number of turns needed to determine the heaviest box?
b) what is the min number of turns ...
- 75.8k
5
votes
Accepted
Minimum keystrokes
I initially thought that copying and pasting individual words/character strings might be beneficial, but since every Ctrl + C and Ctrl + V is counted as two keypresses, it would only make sense if the ...
- 25.7k
2
votes
Minimum function optimization puzzle #3: 3 functions
A short program in R confirms @DanielMathias answer.
You can try the code here.
The code in text: (not showing correctly because of characters '<' and '>')
...
- 6,153
4
votes
Accepted
Minimum function optimization puzzle #3: 3 functions
The minimum number of steps is
With the sequence
My approach: work backwards from the goal.
The final step must be
Apply the inverse of h(x) repeatedly and look for values that are near a square.
...
- 13.4k
1
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Accepted
1
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4
votes
Accepted
Is my solution to a mathematics puzzle I created the most efficient solution there is to it?
Let's see what an optimal path would look like. For starters,
- 8,194
1
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Button multi arm bandit problem
The value under the optimal subsequent strategy of testing a new lever is a least as good as any particular strategy that tests a new lever on the next step. We will consider the particular strategy ...
- 2,976
3
votes
Button multi arm bandit problem
You can solve the problem via dynamic programming as follows. Let $B=\{0,\dots,9\}$ be the set of buttons, and let $r_i$ be the reward for button $i\in B$. Let value function $V(S,d)$ denote the ...
- 11.9k
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