# Tag Info

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 ...
1 vote

### 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) ...
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 ...

### 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 ...

### 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 ...

### 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 ...
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:
Accepted

### Minimum function optimization puzzle #4: Using negative numbers?

It can be done in

### 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.
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 ...
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 ...

### 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 '>') ...
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. ...
1 vote
Accepted

### Minimum function optimization puzzle #2

We can reuse the strategy from the previous question.
1 vote

### Minimum function optimization puzzle #2

This is going to take more words than I would like.
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,
1 vote

### 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 ...
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 ...