Old Tom stands out as one of the smartest folks in the village. Yet, as he sat down to write his last will, Tom ran into a problem he couldn’t solve. Tom owns a very rich piece of land that he needs to split among his three sons in specific amounts. Tom’s apple orchard – 16 plots laid out in a perfect 4×4 square – has to be divided so that each son’s land stays in one piece, with no parts cut off from the rest.
Tom faced what looked like an easy job. He chose to give his land to his sons based on how much they helped him in recent years. His oldest Jake, would get 7 plots for working on his dad’s land for fifteen years. Marcus, the middle son, earned 6 plots after eight years of help, while Peter, the youngest deserved 3 plots for working two summers.
But here’s what stumped everyone: each son’s share had to be one connected piece of land. No scattered plots allowed. Each part needed to form a single unbroken shape where you could walk from any plot to any other within that son’s area.
Tom spent hours drawing combinations. His neighbor Bill said it couldn’t be done. His wife Martha filled pages with failed attempts over two days. Even Jake, who was good with numbers, gave up after a week.
“You can’t fit 7 connected parts, 6 connected parts, and 3 connected parts on a 4×4 grid,” everyone agreed.
Tom didn’t back down. Scattered pieces of land would cause problems and endless disputes over property lines. As the sun set on the tenth day, he had a flash of insight that solved the puzzle everyone had struggled with for weeks.
Can you figure out how Tom divided the 16 sections among his three sons making sure each inheritance stayed in one piece?
Challenge: Draw a 4×4 grid and try to split it into three linked shapes of 7, 6, and 3 squares each. Remember: linked means you can move between squares going up down, left, or right – but diagonal moves don’t count.
| T | T | T | T |
| T | T | T | T |
| T | T | T | T |
| T | T | T | T |
View the answer
SOLUTION:
The solution was to create more creative, interlocking patterns like following:
| J | J | J | M |
| J | J | P | M |
| J | P | P | M |
| J | M | M | M |
Where:
- J = Jake (7 sections): Forms an inverted L-shape along the left side and top
- M = Marcus (6 sections): Creates a backwards L-shape on the right and bottom
- P = Peter (3 sections): Gets a small connected block in the middle
Each son’s land is perfectly connected, and the numbers work out exactly: 7 + 6 + 3 = 16 sections.
