26 Oct
2019
26 Oct
'19
11:55 a.m.
I'm afraid I am still baffled. You still never define the "minimal pieces" constraint. Bob is trying to maximize the sum, and produces a chunking with a great big sum. Alice says, "No, no!" and counters with a different chunking with a smaller sum. It is obvious why Bob prefers his choice: his sum is bigger. It is NOT obvious why Alice prefers hers. At this point, the "minimal pieces" constraint is always mentioned to explain Alice's demurral, but even with a half dozen examples in front of me, I cannot guess what that constraint is.I admit this may be because I am not intelligent enough. But -- they say you don't know how to explain something until you can explain it to the unintelligent. On Sat, Oct 26, 2019 at 11:22 AM Éric Angelini <bk263401@skynet.be> wrote: > Another example, Allan: > (same task -- "10 blocks") > > I was very proud of the integer 46385297110 > that arises when you glue together the blocks > 4.6.3.8.5.2.9.7.1.10 > For me, this integer could only be chunked in > 463+852+97110 sum 98029 > Then came Alice (my feminine part) laughing: > -- Ah, you've overlooked this "minimal pieces" > arrangement: > 4+6+38+52+97+110 sum (ridiculous) > Well... only by swapping the first two blocks I got: > 64385297110. > And now, Alice, what do you say? > Mmmmmh... > 6+43+85+297+110 no (first rule) > (let's start from the back with the "plus" signs): > 6+4+38+52+97+110 no (first rule again) > 6+438+529+7110 sum 8083... better but very low > I had to search more and swap elsewhere: > "Let's try this with me Alice please!" (if you can't > beat them, join them): > 65384297110 > 6+53+84+297110 = ... huge! But wait... > 6+53+842+97110 is the "minimal pieces" solution, waow! > sum = 98011 > Etc. > Best, > É. > (and A) > > > > > > > Le 26 octobre 2019 à 16:57, Éric Angelini <bk263401@skynet.be> a écrit : > > > > > > You're right, Allan, I have problems in defining that rule -- > > which seems obvious when you work with it, but hard to explain > > (please someone, help!-) > > > > Here are a few examples, taken from my search of the "ten blocks" > > maximum weight: > > > > I started with 1,2,3,4,5,6,7,8,9,10 -- untouched, sum 55 > > then 10,9,8,7,6,5,4,3,2,1 -- blocks must be reorganized: > > try: 10, 98, 765, 4321 -- sum 5194 > > (I cannot reorganize in 109, 876, 5432, 1 as the "pieces" are > > not increasing from left to right -- BUT I cannot either > > reorganize in 10, 987654321 with sum 987654331 because > > Alice will tell me: "Too easy, pal! There is a way to break > > that in "minimal pieces!" And she would be right, of course > > with the solution above: 10, 98, 765, 4321 -- sum 5194. > > In short, Alice will always try to show me that the block > > ordering I've selected (among a huge lot of others -- > > factorial 10) can be "disassembled" to reduce the sum I was > > so proud of (the first constraint being still ok) > > Dunno if this helps... > > Best, > > É. > > > > > > > > > > > > > > > Le 26 octobre 2019 à 16:08, Allan Wechsler <acwacw@gmail.com> a > écrit : > > > > > > > > > Please clarify the "minimal pieces" constraint? Everything seems to > depend > > > on that, and I cannot infer what it is from the examples given. > > > > > > On Sat, Oct 26, 2019, 6:16 AM Éric Angelini <bk263401@skynet.be> > wrote: > > > > > > > Hello Math-Fun, > > > > Alice and Bob play the "Chunk & Sum" game. > > > > Which consist in A giving to B an integer and asking B to chunk it in > > > > smaller pieces that must be increasing from left to right. > > > > Example: > > > > 3223584222 is given by A to B. > > > > B chunks it like this: 3 22 358 4222. > > > > The "weight" of a partition is given by the sum of the pieces: 3 + > 22 + > > > > 358 + 4222 = 4605 > > > > The aim of B is to produce the highest weight. > > > > The aim of A is to warn B, because his partition must obey a precise > > > > "minimal pieces" rule: > > > > "Hey, Bob, your partition is bad, this is the right one: 3 + 22 + 35 > + 84 > > > > + 222 = 366". > > > > B agrees, his first partition forgot the "minimal pieces" way to > chunk. > > > > > > > > After a while, Alice and Bob have an idea: to give to each other > wooden > > > > blocks instead of integers -- blocks with numbers printed on them. > > > > A receives the blocks marked 1, 2, 3, 4, 5. > > > > B receives the blocks marked 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. > > > > The game consists now to put one's blocks in a certain order on the > table > > > > such to produce a number to chunk – this number having the highest > weight > > > > according to the two rules we have just seen: > > > > 1) pieces in increasing order from left to right > > > > 2) "minimal pieces". > > > > Alice forms the integer 43521 with her blocks and claims that among > the > > > > 120 possible solutions, this is the best one. Indeed, the only way to > > > > properly chunk 43521 is 43 + 521 = 564 and 564 is the maximum you > can reach. > > > > What is the integer Bob should form with his set of blocks in order > to > > > > maximize the weight? > > > > ____________________ > > > > (warning: this is hard to compute by hand, my best result is over > 100,000 > > > > -- took me the night) > > > > (note that the 1 and the 0 of the block marked 10 cannot be > separated) > > > > This idea could produce a nice little sequence for the OEIS: "Highest > > > > possible weight that one can reach with blocks marked 1 to n, > according to > > > > the Chunk & Sum game". I guess the sequence would start like this: > 1, 21, > > > > 33, 325, 564,... (not in the OEIS, if the hereunder computations are > ok) > > > > n = 1 --> integer produced is 1 with weight = 1 > > > > n = 2 --> integer produced is 21 with weight = 21 > > > > n = 3 --> integer produced is 231 with weight = 2 + 31 = 33 > > > > n = 4 --> integer produced is 4321 with weight = 4 + 321 = 325 > > > > n = 5 --> integer produced is 43521 with weight = 43 + 521 = 564 > > > > etc. > > > > My solution for n = 10 is here, with Daniel Day-Lewis, on my > personal blog: > > > > https://bit.ly/31KVedK) > > > > Best, > > > > É. > > > > > > > > _______________________________________________ > > > > math-fun mailing list > > > > math-fun@mailman.xmission.com > > > > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > > > > > > _______________________________________________ > > > math-fun mailing list > > > math-fun@mailman.xmission.com > > > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > > > _______________________________________________ > > math-fun mailing list > > math-fun@mailman.xmission.com > > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > _______________________________________________ > math-fun mailing list > math-fun@mailman.xmission.com > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >