How Will the Son Break Off Links for 123 Weeks Without Skipping a Week?

[MasterBlaster]

Brain Teaser #4??

What is the explanation. It seems totally incorrect.

If the son is going to stay 123 weeks - and each week he HAS TO break off new links.

Then he MUST break off something each of the 123 weeks.

Explain the question...

 

[MasterBlaster]

See, no one knows the answer becaue it's wrong!

 

[Matt]

The minimum number of cuts needed to be made is 4 for a chain with 89 links.
If the links are numbered serially from 1 to 89, then the cuts would be made on the following links:
6, 17, 38, and 79.

This would result in 4 one-link pieces, one 5-link piece, one 10-link piece, one 20-link piece, one 40-link piece, and one 10 piece.

To gain a better understandstanding, consider the scenario in the first few weeks as illustrated in the table below.

Weeks: Gold Links Given:
1 1
2 1 + 1
3 1 + 1 + 1
4 1 + 1 + 1 + 1
5 5
6 5 + 1
7 5 + 1 + 1
8 5 + 1 + 1 + 1
9 5 + 1 + 1 + 1 + 1
10 10
11 10 + 1
12 10 + 1


The table above indicates that:
at the end of the fifth week, the 5-link piece is given and the 4 one-link pieces are taken back;
at the end of the tenth week, the 10-link piece is given and the 4 one-link pieces as well as the 5-link piece are taken back.

 

[Matt]

Edit: 12 - 10 + 1 + 1