The minimum number of cuts needed to be made is 4. If the links are numbered from 1 to 123, then the cuts would be made on the following links: 6, 17, 38, and 79.
This would result in four 1-link pieces, one 5 link piece, one 10-link piece, one 20-link piece, one 40-link piece, and one 44 piece.
Sponsored Video Stories from LifeZette
Today's brain teaser courtesy of Braingle.com.