4 ms·

Sometimes when I am at the gym I wonder if there could be a better set of weight denominations. I feel like 1,3,9,27,81 could be an optimal set; but I am not

Sometimes when I am at the gym I wonder if there could be a better set of weight denominations. I feel like 1,3,9,27,81 could be an optimal set; but I am not sure how to prove it.

ChadNauseam 2y ago
Since every positive even integer is the sum of two primes (at least, within the range of weights you're likely to be lifting), maybe [5, ...the list of primes times 5]? So if the list of primes is 2, 3, 5, 7, 11, etc, you could have weights of 5, 25, 35, 55, 75, 11*5, etc. for 5, 10, 15, 25, 35, 55, etc.
- gpm 2y ago
  > So if the list of primes is 2, 3, 5, 7, 11, etc, you could have weights of 5, 2*5, 3*5, 5*5, 7*5, 11*5, etc. for 5, 10, 15, 25, 35, 55, etc. Fixed the formatting for you. You need to put a \ before * symbols to have them reliably render in HN
  - latexr 2y ago
    > You need to put a \ before * symbols to have them reliably render in HN Alternatively, write two sequential *, like so: **
contravariant 2y ago
Optimal in what sense? If you want to have each whole number using each number at most twice then sure. If you want to get within x% using at most k weights the some kind of logarithmic distribution is also a good bet. Both you and OP could benefit from being a bit clearer about what you find optimal.
- jstrieb 2y ago
  See this comment for a more in-depth explanation of what I meant by "optimal" for poker chip denominations. Hopefully that clarifies. That comment has a link to the code if it's still not clear enough. https://news.ycombinator.com/item?id=40576198 https://news.ycombinator.com/item?id=40576198
alex-mohr 2y ago
J. Shallit (2003). "What this country needs is an 18c piece" (PDF). Mathematical Intelligencer. 25 (2): 20–23.
- dang 2y ago
  What readers of your comment need is two HN thread references :) What This Country Needs is an 18¢ Piece (2002) [pdf] - https://news.ycombinator.com/item?id=38665334 https://news.ycombinator.com/item?id=38665334 - Dec 2023 (272 comments) What This Country Needs Is an 18¢ Piece [pdf] - https://news.ycombinator.com/item?id=14579635 https://news.ycombinator.com/item?id=14579635 - June 2017 (45 comments)
aidenn0 2y ago
By the time I'm on my third set, math with multiples of 5 is hard; please don't make me use those...

Sometimes when I am at the gym I wonder if there could be a better set of weight denominations. I feel like 1,3,9,27,81 could be an optimal set; but I am not sure how to prove it.

ChadNauseam 2y ago

Since every positive even integer is the sum of two primes (at least, within the range of weights you're likely to be lifting), maybe [5, ...the list of primes times 5]? So if the list of primes is 2, 3, 5, 7, 11, etc, you could have weights of 5, 25, 35, 55, 75, 11*5, etc. for 5, 10, 15, 25, 35, 55, etc.

gpm 2y ago
> So if the list of primes is 2, 3, 5, 7, 11, etc, you could have weights of 5, 2*5, 3*5, 5*5, 7*5, 11*5, etc. for 5, 10, 15, 25, 35, 55, etc. Fixed the formatting for you. You need to put a \ before * symbols to have them reliably render in HN
- latexr 2y ago
  > You need to put a \ before * symbols to have them reliably render in HN Alternatively, write two sequential *, like so: **

contravariant 2y ago

Optimal in what sense? If you want to have each whole number using each number at most twice then sure. If you want to get within x% using at most k weights the some kind of logarithmic distribution is also a good bet. Both you and OP could benefit from being a bit clearer about what you find optimal.

jstrieb 2y ago
See this comment for a more in-depth explanation of what I meant by "optimal" for poker chip denominations. Hopefully that clarifies. That comment has a link to the code if it's still not clear enough. https://news.ycombinator.com/item?id=40576198 https://news.ycombinator.com/item?id=40576198

alex-mohr 2y ago

J. Shallit (2003). "What this country needs is an 18c piece" (PDF). Mathematical Intelligencer. 25 (2): 20–23.

dang 2y ago
What readers of your comment need is two HN thread references :) What This Country Needs is an 18¢ Piece (2002) [pdf] - https://news.ycombinator.com/item?id=38665334 https://news.ycombinator.com/item?id=38665334 - Dec 2023 (272 comments) What This Country Needs Is an 18¢ Piece [pdf] - https://news.ycombinator.com/item?id=14579635 https://news.ycombinator.com/item?id=14579635 - June 2017 (45 comments)

aidenn0 2y ago

By the time I'm on my third set, math with multiples of 5 is hard; please don't make me use those...