Kvant Math Problem 824

Verified: no
Verdicts: SKIP + SKIP
Solve time: 4m20s
Source on kvant.digital

Problem

In the grid shown in Figure 3, each cell has size $1\times 1$. Is it possible to represent this grid as a union of

1. a) 8 broken lines of length 5;
2. b) 5 broken lines of length 8? (8)

Figure 3

N. I. Avilov

All-Union Mathematical Olympiad for School Students (1983, Grade 8)

I need the diagram from Figure 3 to solve the problem rigorously.

The statement refers to “the grid shown in Figure 3,” but the figure itself is not included in your message. Whether the decomposition is possible depends entirely on the exact shape of that grid.

Please upload Figure 3 (or provide a clear description of the grid), and I will write the solution in the six required sections:

Exploration

Problem Understanding

Proof Architecture

Solution

Verification of Key Steps

Alternative Approaches