In a 5-digit number, last digit is 3 times the first one. 3rd digit is 3 less…

Concept: When a digit-relationship puzzle states relationships between digits without enough constraints to pin down a single 5-digit number on its own, check each candidate number against every stated relationship simultaneously - the correct one is the only candidate that satisfies all of them at once.

Application: check each option against the three relationships.

1. From the conditions, if the first digit is d1 and the second digit is d2, the number must have its last digit equal to 3 x d1, its third digit equal to d2 minus 3, and its fourth digit equal to d2 plus 4.

2. Check 25296: first digit 2, second digit 5 - last digit is 6 (matches 3 x 2), third digit is 2 (matches 5 minus 3), fourth digit is 9 (matches 5 plus 4). All three relationships hold.

3. Check 26594: first digit 2, second digit 6 - the last digit (4), third digit (5), and fourth digit (9) each fail to match what the three relationships require.

4. Check 24569: first digit 2, second digit 4 - the last digit (9), third digit (5), and fourth digit (6) each fail to match what the three relationships require.

5. Check 26458: first digit 2, second digit 6 - the last digit (8), third digit (4), and fourth digit (5) each fail to match what the three relationships require.

Cross-check: 25296 is the only one of the four numbers where the last, third, and fourth digits simultaneously satisfy all three stated relationships to the first and second digits, confirming it as the answer.