Henry Ernest Dudeney/Puzzles and Curious Problems/54 - The Birth of Boadicea/Solution

by : $54$

 * The Birth of Boadicea
 * A correspondent (R.D.) proposes the following little puzzle:


 *  died $129$ years after was born.
 * Their united ages (that is, the combined years of their complete lives) were $100$ years.
 * Cleopatra died 30.
 * When was Boadicea born?

Solution
She was born in 1.

Proof
Let $C_b$, $C_d$, $B_b$, $B_d$ denote the years of birth and death of Cleopatra and Boadicea respectively.

We have: