Logic puzzles can get complicated, and keeping track of information while you're sleuthing is no easy task. See how grids can help you efficiently deduce your way to the truth.

May 15 | May 16 | May 19 |

June 17 | June 18 | |

July 14 | July 16 | |

August 14 | August 15 | August 17 |

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.

Bernard: At first I don't know when Cheryl's birthday is, but I know now.

Albert: Then I also know when Cheryl's birthday is.

So, when is Cheryl's birthday?

\[\begin{matrix} \textbf{Andy}: & \textit{(A1)} & \text{The number is less than 12}\\ & \textit{(A2)} & \text{7 does not divide the number}\\ & \textit{(A3)} & \text{5 times the number is less than 70}\\ \textbf{Becky}: & \textit{(B1)} & \text{12 times the number is greater than 1000}\\ & \textit{(B2)} & \text{10 divides the number}\\ & \textit{(B3)} & \text{The number is greater than 100}\\ \textbf{Chloe} : & \textit{(C1)} & \text{4 divides the number}\\ & \textit{(C2)} & \text{11 times the number is less than 1000}\\ & \textit{(C3)} & \text{9 divides the number}\\ \textbf{Danny} : & \textit{(D1)} & \text{The number is less than 20}\\ & \textit{(D2)} & \text{The number is a prime number}\\ & \textit{(D3)} & \text{7 divides the number} \end{matrix}\]

What is their favorite number?

Let the number that takes place of the cell marked \(A\) be denoted \(A\), and so forth.

What is the value of \(A+B+C\)?

- The blue number tells the number of colors in my guess that exist in the secret pattern, which are also correct in position.
- The white number tells the number of colors in my guess that exist in the secret pattern, but which are incorrect in position.

When where there should be a number, it is empty instead, the number is assumed to be zero.

What is the secret pattern? Enter your answer in order from left to right, translating the color to a digit code according to this table:

Color | Green | Blue | Yellow | White |

Code | 1 | 2 | 3 | 4 |

Color | Black | Red | Purple | Orange |

Code | 5 | 6 | 7 | 8 |

As an example, if the answer is orange-blue-yellow-white-black, enter \(82345\).

If my house number is a multiple of 3, then it is a number from 50 to 59.

If my house number is not a multiple of 4, then it is a number from 60 to 69.

If my house number is not a multiple of 6, then it is a number from 70 to 79.

Can you determine the professor's house number?

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