Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Time to Evolve

We had an interesting anonymous solution to this problem, giving rise to some sensible numbers. We think that similar investigations would make for interesting data-handling project work.

We used the internet to research lifespans. We were surprised to see that fishes and reptiles live for a very long time. A modern day bony fish is the sturgeon, from which caviar is taken. Lizards seem to have quite a wide range of lifespans (between 10 and 50), so we picked 30 as an average. The numbers for dingos and lemurs seemed typical for these sorts of creatures. We also changed the human numbers because in the past both would be smaller. Our table became

@

## You may also like

### Ladder and Cube

### Archimedes and Numerical Roots

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

Age 14 to 16

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

We had an interesting anonymous solution to this problem, giving rise to some sensible numbers. We think that similar investigations would make for interesting data-handling project work.

We used the internet to research lifespans. We were surprised to see that fishes and reptiles live for a very long time. A modern day bony fish is the sturgeon, from which caviar is taken. Lizards seem to have quite a wide range of lifespans (between 10 and 50), so we picked 30 as an average. The numbers for dingos and lemurs seemed typical for these sorts of creatures. We also changed the human numbers because in the past both would be smaller. Our table became

@

Creature | Timespan | Time to maturity | Lifespan | Min number | Max number | Average number |

Fishes | 50,000,000 | 20 | 100 | 500,000 | 2,500,000 | 833,333 |

Amphibians | 50,000,000 | 20 | 100 | 500,000 | 2,500,000 | 833,333 |

Reptiles | 100,000,000 | 2 | 30 | 3,333,333 | 50,000,000 | 6,250,000 |

Early mammals | 125,000,000 | 2 | 10 | 12,500,000 | 62,500,000 | 20,833,333 |

Mammals | 60,000,000 | 2 | 25 | 2,400,000 | 30,000,000 | 4,444,444 |

Apes | 14,000,000 | 2 | 35 | 400,000 | 7,000,000 | 756,757 |

Humans | 1,000,000 | 13 | 40 | 25,000 | 76,923 | 37,736 |

To get the minimum number of ancestors for each row we divided the time in years by the lifespan. To get the largest numbers of ancestors we divded the time in years by the time to maturity.

This gave grand totals of between $19,658,333$ and $154,576,923$ ancestors.

To get the average age of an ancestor when giving birth we found an average age = (Lifespan + time to maturity)/2 and timesed this by the timespan.

Assuming that ancestors were born at an average point in their parents' lives, we get $33,988,937$ ancestors.

Rounding up to sensible values, we think that there were at most $150$ million ancestors, at least $20$ million ancestors and probably about $35$ million ancestors.

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?