Optimal way to cut boards to given length

Introduction

Problem: Need to cut 6×110 cm similar pieces from 4×200 cm wood. The parts can be glued together, but the gluing should be somehow symmetrical. Also the kerf (the width of the blade) should be considered.

Problem 2: We are given a stick of length L. We make cuts such that the longest piece is of length n at most. What are the minimum number of pieces we will get and in how many ways this can be done? https://math.stackexchange.com/questions/2268572/number-of-ways-of-cutting-a-stick-such-that-the-longest-portion-is-of-length-n

Problem Sandwich https://www.codechef.com/MAY17/problems/SANDWICH

Cutting stick problem We are given a bundle of sticks all having integer lengths. Can we break the sticks so that the resulting sticks have lengths 1, 2, . . . , n? https://www.cse.iitb.ac.in/~jagadish/cutting_sticks_ipl.pdf https://iwriteiam.nl/cutsticks.html

Problem Minimize number of cuts required to break N length stick into N unit length sticks. https://www.geeksforgeeks.org/dsa/minimize-number-of-cuts-required-to-break-n-length-stick-into-n-unit-length-sticks/

Problem Number of ways to cut a stick of length N into in even length at most K units long pieces https://www.geeksforgeeks.org/dsa/number-of-ways-to-cut-a-stick-of-length-n-into-in-even-length-at-most-k-units-long-pieces/

Optimization

Consider

References

https://bland.ltd/cutlist/ (https://jonathan.overholt.org/projects/cutlist)