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CaptainEd

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1. "Flipping" Dimes and Pennies

I can do it in 8
2. Green and Yellow hats

As always, we hope for some communication. The prisoners can see each other. It’s not clear they can hear each other (after all, if they shout simultaneously, they can’t benefit from hearing the others). Are they allowed to turn their bodies to face in a variety of directions, or some such thing? You said “no communication”, and I fear you mean it, but just askin’...
3. Jelly beans join the clean plate club

Here’s a tiny observation about what the next to last step looks like.
4. Waiting, again II

much more clearly stated than my babbling. I’m tickled that I’ve shown that it can be evaluated one flip at a time, based merely on the parity of contiguous Hs. here is my argument, expressed by plagiarizing your expression: Let e be the expected number of flips from the initial (even) state There are two states that are easy to analyze and cover all the possibilities: E is the initial state, it also represents the state of having seen an even number of H (including zero), since the beginning or the most recent T. O is the odd state, representing the fact of having seen an odd contiguous run of H. State E requires e more flips. In this state, H changes to state O, while T remains in state E State O requires o more flips. In this state, H changes to state E, while T terminates with a win. That allows us to write an expression for x as the sum of these terms, weighted by their respective probabilities, all 1/2. e = 1/2{1+e} + 1/2{1+o} o = 1/2{1+e} + 1/2 substitute o into e e = 1/2{1+e} + 1/2{1+1/2{1+e} + 1/2} = 1/2{1+e} + 1/2+1/4+e/4 + 1/4 = 3/2 + 3e/4 e/4 = 3/2 e = 6

8. Waiting, again

Gardner sets high standard in many ways. I was a child reading Childrens Activities and a few years later I was enjoying hexaflexagons and later mathematical games. I was kneeling behind you in worship. i enjoy the puzzles here, and sometimes I don’t understand something that is obvious to anyone else. I think I may have a touch of ambiguity flu. Keep on puzzling, Bonanova!
9. Waiting, again

Thank you Bonanova, sorry to be so dense
10. Waiting, again

I want to be sure I’ve got this right. There are six (presumably distinguishable) dice. I want to demonstrate that each is capable of showing all six faces. Paul lets me roll all six (and tabulate which individual dice showed which numbers) charges \$1 for the combined roll, and pays \$50 when the tabulations show each die has shown all six faces. Peter has me roll one die at a time, charges \$1 for the individual roll, tabulates the results, and pays \$20 when each die has shown all six faces. OR... my Termination condition is seeing all six numbers on the table at once. Paul has me roll all 6 dice each time, and only pays me if I roll a full straight (123456). Peter lets me roll one die at a time, once I’ve rolled all six dice, he lets me improve my hand by rolling a single die that duplicates another one, and pays once all six numbers are showing.

Perhaps
12. Adapting a classic crossing puzzle

Good job slashpuzzler! And neat puzzle BMAD!
13. Two can tango

Nice job, araver! Nice puzzle, bonanova
14. Soldiers in a field

Maybe this is clearer and more accurate than my previous try. Point one:
15. Line splitting

It's been a long time. Here's a recharacterization that recognizes a much smaller search space: Overview Definitions and additional constraint LineSplittingMValues.xlsx BonanovaSequence.xlsx
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