Samir has a 23-link chain. He wants to cut and disengage the minimum number of links so that any number of links from 1 to 23 can be obtained by taking one or more of the resulting pieces (including the disengaged links). Give the position(s) of the link(s) he must cut.

Guest Feb 9, 2021

#1**+1 **

1. First cut must be at the 3-rd link. Then Samir has this 3-rd link cut as a single link; he has also the block of 2 links (the 1-st and the 2-nd links connected together); and then he has 3 links as the union ((1st + 2nd together) U 3rd).

2. Next cut must be at the 8-th link. Then, in addition to the set (A), Samir has - this 8-th link cut; - the block of 4 links (4th+5th+6th+7th all connected together), and then it is clear that combining this block of 4 links with what he just has in the set (A), he is able to have a) 4 links; b) 5=4+1 links; c) 6=4+2 links; d) 7=4+3 links; and e) 8=4+3+1(8th) links.

3. By continuing with this pattern, it is clear that (C) the next, third cut must be at the 8 + 8 + 1 = 17-th link.

4. The next (and the last), fourth cut must be at the 17 + 3 = 20-th link. Then it is OBVIOUS that having the sets (A), (B), (C) and additional 2 connected segments (18,19) and (21,22,23) and 1 cut link (20th) Samir will be able to present a) 18 = 17 +1; b) 19 = 17+2; c) 20 = 17+2+1; d) 21=17+3+1; e) 22=17+2+3; and, finally, all 23 links as well.

**So, the problem is just solved and the ANSWER is: The cuts should be made at 3-rd; 8-th; 17-th; and 20-th links.**

Hope this helped!

( ﾟдﾟ)つ Bye

TaliaArticula Feb 9, 2021