Anyone else ever go to 538’s Riddler or Riddler Express? I enjoy some of the challenges though most of them i just skip because i haven’t the foggiest idea how to solve. That was not the case for last friday’s riddler express.
As an aside, does GoActuary support LaTex and the [spoiler][/spoiler] tag formatting?
Is this straightforward? Can’t you just ignore all the instances where you don’t win? Because there are two conditions for winning. You either successfully land three conservative throws, or you land one aggressive throw. So, then you work out the 8 combinations where you win, then take the maximum probability from those 8 scenarios. Is it that simple? It’s been a while since exam P and even longer since combinatorics in college, so I’m rusty. Also I believe the highest probability of a win is 51.2%
I think the highest probability of a win is considerably above 51.2%, because you know the result of each toss before making the next. So there’s a 40% chance you win with a 3 on toss 1 (aggressive) because then you waste the rest. Add 12% for an aggressive complete miss then an aggressive 3. Just those get you to 52%. Then you have the 30% chance of a 1 on first toss, plus 2 1’s thereafter, and some other chances.
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I get 85.48% for throwing aggressive until 1 point or 3, then either conservative or wasted thereafter, depending on where you are.
I didn’t evaluate tries starting with conservative.
Do spoilers with (using brackets instead of parens)
(details=stoilertext)
what you want hidden
(/details)
You may well need the tags on separate lines from the material to be spoilered.
I know I’ve seen that latex is possible here. Possibly used it. Don’t remember how
Lots of tips about Latex. Thread claims it works (except in signatures). As with spoilers, tags may have to be on separate lines. (That thread seems to say they must be.)
Bump…
For this week’s (4/29/2022) numerical puzzler:
I sometimes read these to see how to solve them, but don’t normally take time out of my busy posting schedule.
Riddler Express
There are many fractions with a numerator of 1 whose decimal expansions don’t go on to infinitely many decimal places. For example, 1/4 is equivalent to the decimal 0.25, and 1/500 is equivalent to 0.00. However, the decimal expansion of 1/3 is 0.33333 …, a decimal that never terminates.
If you were to add up all these numbers — fractions with a numerator of 1 whose decimal expansions don’t go on forever — what would be the sum? (Note: Before you ask, let’s include the fraction 1/1 in this group.)
I thought this was pretty easy.
My answer:
Summary
2.5
My reckonin’:
Only numbers with denominators that are factors of ONLY 2 and 5 qualify, cuz, Base 10.
Solution = Sum (i=0 to infinity) {Sum (j=0 to infinity) (1/5^i * 1/2^j)}
(If someone wants to mathify that equation, that would be awesome.)
Each j Sum is 1/5^i * 2
So, factor the 2 to the front, and you get:
2 * Sum (i=0 to infinity) (1/5^i )
= 2 * 1/(1-(1/5)) = 2 * 5/4 = 2.5
Somebody please check my math, as I could forget to carry the 1, mghey.
Of course, the answer could also be 0, since there is a negative fraction for each positive fraction.