What does "masses $1$ through $n$" mean?

Question

Mathematical Chunks of Sentient Protoplasm (MCSPs, for short) are smart blobs who dream of merging together into one huge blob. But they can only do it following certain rules:

1) If two MCSPs have the same mass, or if their masses are 1 apart, they can merge into a single MCSP, whose mass will be the sum of the original two.

2) If an MCSP has even mass, it can split into two MCSPs, each with half the original mass.

Suppose we start with $n$ MCSPs, with masses $1$ through $n$. For what values of n is there a finite sequence of steps that will allow all n MCSPs to merge together into a single MCSP and achieve their dream of unity?

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What does with masses through n mean?

It's an American way of saying that there are $n$ blobs with masses $1,2,\ldots n$ (one of each). British English would phrase it as "there are $n$ blobs with distinct integer masses from $1$ to $n$." — postmortes, Feb 24 '20 at 10:45
@postmortes I'm British and I would also use "$1$ through $n$" or "$1$ to $n$" to mean $1,\ldots,n$ — lioness99a, Feb 24 '20 at 10:47
After you ask a question here, if you get an acceptable answer, you should "accept" the answer by clicking the check mark $\checkmark$ next to it. This scores points for you and for the person who answered your question. You can find out more about accepting answers here: How do I accept an answer?, Why should we accept answers?, What should I do if someone answers my question?. — Shaun, Feb 24 '20 at 10:48
@lioness99a thank-you for the anecdatum :) However, generally there is a dialectal difference. — postmortes, Feb 24 '20 at 11:05

score 1 · Answer 1 · edited Mar 07 '20 at 00:18

1

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edited Mar 07 '20 at 00:18

ViktorStein

4,838

answered Mar 06 '20 at 23:11

Marisa Debowsky

11

score 0 · Accepted Answer · answered Feb 24 '20 at 10:46

0

Here

with masses $1$ through $n$

means that the $n$ masses take the values from $1$ to $n$. So there's one mass with value $1$, one with value $2$, etc.

answered Feb 24 '20 at 10:46

Shaun

44,997

Also , please clarify what does that “ if their masses are 1 apart “ means?
Sorry for asking such silly questions but since English isn’t my primary language I struggle with it a bit.
– Evan_Smith Feb 24 '20 at 17:32
It means that there is some $m$ such that the masses are $m, m+1, \dots, m+(n-1)$, @Evan_Smith. – Shaun Feb 24 '20 at 17:39

What does "masses $1$ through $n$" mean?

2 Answers2