harlie's Number
"Using clues 2 and 4, we realised that our number had to be 3 digits long. Using clue 3, we initially worked out that our number need to end in 3, 5, 7 or 9. As Charlie's number is palindromic, the third and first digits need to be the same. Therefore, due to rule 5, our first and third digits had to be 3 (to make sure our number is less than 500). Finally, using rule 3, we used 8 as our second digit (to make the difference between the largest and smallest digits 5). We used the rest of the rules to check our number to see if it worked. 383 is a prime number and therefore will only have two divisors (itself and one and NOT 3)."
Tower problem
"Rule one meant we started with a yellow cube on top. We then placed a red cube on top of a green cube and placed this below the yellow - for rule two and part of rule three. We both blue cubes on the outside faces of our green cube - for rule four. Finally, we placed a yellow cube underneath the red to satisfy all the rules. Realising that "above" did not necessarily mean "directly above"/"touching", made this problem a lot easier.
We then tried to create a tower which was a single cube wide. By placing both blue cubes either side of the green cube, we satisfied rule 4. Placing a red cube above a blue cube satisfied rule two. Placing a yellow cube on the top and bottom of the tower satisfied the remaining rules."