Question 9
A $5\times5$ table is called a UCAS table if it satisfies the following conditions:
- Each cell is coloured with grey or white,
- Any two adjacent cells (sharing an edge) must have different colours,
- The 25 cells are filled with 25 consecutive integers, which must include 2024,
- The numbers in any two adjacent cells (sharing an edge) must have different parity (cannot be both odd or both even).
Now, your tasks are to:
a. Construct a UCAS table which gives the greatest possible sum of all integers in the shaded cells. What is the sum?
b. Construct a UCAS table which gives the smallest possible sum of all integers in the shaded cells. What is the sum?
- Each cell is coloured with grey or white,
- Any two adjacent cells (sharing an edge) must have different colours,
- The 25 cells are filled with 25 consecutive integers, which must include 2024,
- The numbers in any two adjacent cells (sharing an edge) must have different parity (cannot be both odd or both even).
Now, your tasks are to:
a. Construct a UCAS table which gives the greatest possible sum of all integers in the shaded cells. What is the sum?
b. Construct a UCAS table which gives the smallest possible sum of all integers in the shaded cells. What is the sum?