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

Puzzles and Curious Problems by Henry Ernest Dudeney: $54$

Boadicea died $129$ years after Cleopatra was born.

Their united ages (that is, the combined years of their complete lives) were $100$ years.

Cleopatra died $\text {30}$ $\text {BCE}$.

When was Boadicea born?

She was born in $\text {1}$ $\text {BCE}$.

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

We have:

$\ds B_d - C_b$

$=$

$\ds 129$

Boadicea died $129$ years after Cleopatra was born.

$\ds \paren {B_d - B_b} + \paren {C_d - C_b}$

$=$

$\ds 100$

Their united ages (that is, the combined years of their complete lives) were $100$ years.

$\ds C_d$

$=$

$\ds -30$

Cleopatra died $\text {30}$ $\text {BCE}$.

$\ds \leadsto \ \ $

$\ds 129 - B_p - 30$

$=$

$\ds 100$

$\ds \leadsto \ \ $

$\ds B_p$

$=$

$\ds -1$

$\blacksquare$