these questions relate to the game of yahtzee.
if you don't know the rules thereof, find someone who does.
1. treating the dice as ordered (which the game itself does not do; 12345 is the same as 24531 as the rules of teh game go, but are different numbers for this example), what roll treated as a five-digit number contains the greatest power of an integer?
2. what is the maximum score possible?
3. what are the maximum and minimum scores if all dice come up the same number (so you might throw all 5s and nothing else) throughout the game?
4. what is the maximum score you could achieve for a game without throwing a yahtzee?
5. what is the minimum score you could get by throwing one yahtzee?
answers will be posted in two weeks unless someone gets them all sooner (to allow others to try, don't post an answer before 02/20).
Originally posted by BarefootChessPlayeryour answers to them as i recall might be as follows: 1. +/- 65432
these questions relate to the game of yahtzee.
if you don't know the rules thereof, find someone who does.
1. treating the dice as ordered (which the game itself does not do; 12345 is the same as 24531 as the rules of teh game go, but are different numbers for this example), what roll treated as a five-digit number contains the greate ...[text shortened]... nless someone gets them all sooner (to allow others to try, don't post an answer before 02/20).
2. 1575 (i think taking into account that you have rolled all yahtzee's)
4. is 301 (a good dart game) 😀
3 and 5 i am not too sure about
Originally posted by rattlerz28two and four are right.
your answers to them as i recall might be as follows: 1. +/- 65432
2. 1575 (i think taking into account that you have rolled all yahtzee's)
4. is 301 (a good dart game) 😀
3 and 5 i am not too sure about
the answer to #1 is not 65432, though.
three and five are both impossible to imagine, but interesting anyway.
a clarification on how the maximum score (#2) is attained:
you first throw five 6s, and score them a yahtzee. you then throw five 3s (these early ones don't matter what you throw five of, but only that you throw five of each once) and put them on your threes. then five ones, and you put those on your ones. remember, though, that each subsequent yahtzee is worth 100 bonus. then come five fives; put them on your fives. another five ones, which you can ue as a joker; put them on large straight. five fours follow, and they go on fours. your top score is now 65, so you rack up your 35 bonus. you throw five threes again, putting them on small straight. five twos for the 2s, five more fives for full house (ironically, they score the same whether taken as full house or four of a kind). then five sixes, which go on sixes. your top score is now 105 plus bonus. you keep throwing nothing but sixes until all spaces are filled, thus getting 30 for each of three and four of a kind and chance. your scorecard will show:
5, 10, 15, 20, 25, 30, 35 bonus, 30, 30, 25. 30, 40, 30, 1250 (fifty for the first yahtzee adn 100 for each after that).
total is 1575.
the odds against such a feat are so astronomical that it is reasonable to say that it won't be achieved even if every person and every computer in the world played the game continuously for millennia!
look at it this way: the odds of throwing a yahtzee with one roll is one in 1296 (6^5, with six different possiblities); with two, between one in six and one in 1296; and with three, i think, one in between six and 216. since some are specific rolls (one each of ones through fives and four sets of sixes), those are one in 7776 each but placed anywhere in the sequence of turns, so i'm taking those at 12 in 7776^9 or two in 6^44. you can see where this is a huge number!
there are other factors involved, of course, but that will do for now.
how do you get 301 with no yahtzees? simply throw four each of ones thrugh sixes for a top of 84 plus bonus, get your straights and full house, and throw 29 (56666) for each of three and four of a kind and chance. the scorecard then shows: 4, 8, 12, 16, 20, 24, 35 bonus, 29, 29, 25, 30, 40, 29, 0, for 301. also highly unlikely; the best i've done in thousands of games is 282, in which i got the three 29s but could manage only 65 on top.
doesn't anyone else play this fun little game and know how to get the combinations i'm referring to?
The maxium score you can get in yahtzee is not 1575 but 1505 because you must zero the small straight and the large straight.
You cannot score these if you have yahtzees.
Also, the minumum score with one yahtzee is 56, that being the yahtzee (50), zero in all the other rows and 6 in chance.😕
Originally posted by yahtzee12the rules allow you to use a second (or more) yahtzee as a joker, meaning you can use it anywhere on the bottom row, so my my original assertion was correct. (the handheld electronic version allows this so it must be right.)
The maximum score you can get in yahtzee is not 1575 but 1505 because you must zero the small straight and the large straight.
You cannot score these if you have yahtzees.
Also, the minumum score with one yahtzee is 56, that being the yahtzee (50), zero in all the other rows and 6 in chance.😕
the only thing you cannot use a second yahtzee for is, say you roll five 6s, you would get no credit for putting them in anything other than 6s on the top row--you would get 100 points for the second yahtzee but no more. i had this happen before--rolled five 5s and 5s were already filled, and there wsa no place to put it but on the top so i zeroed out whatever the cheapest loss was since it was still worth 100 points.
you are right on the 56, however--but i couldn't see that hapening. surely you wouldn't zero out all of your top (say you were going for 4s and didn't roll any, but had one 1 and ones were open. you' probably put your one 1 there instead of zeroing out 4s), and somewhere along the line you'd get a "chance" of more than six! (not only would you be having extremely bad luck, you'd be playing stupidly too!)
the lowest score i've ever gotten with one yahtzee is 152. i was able to get something on the top but no bonus, and some of the rest, but not all that much.
my lowest score without a yahtzee was 76, but because i adopted a new strategy, i am usually guaranteed about 130 even if i cannot get any of the straights and full house. i do get my top bonus about 75% of the time.
my usual score is around 220 though.
any ideas on the other two?
Originally posted by mikenaythat was what i thought too.
I believe 65536 is 2^16 - I'd imagine that's the highest power of an integer available.
by teh way, i realized taht i needed to clarify a little on the last post.
if you throw a second yahtzee and the top slot for that number is open, you cannot use that yahtzee for a straight! (it will score zero plus the 100 bonus!)
if the corresponding number slot on top has been filled, then the yahtzee is a joker and can be placed anywhere except as noted earler.
only one question to go!