Penguin Problems
Some puzzles invented by SYMS member Hugh Robinson.
- There are five penguins called Blotwell, Super, Selwyn, Kite and Herodotus. This chart shows the number of days taken by any penguins together to eat 1 load of Penguin fodder. How many loads are needed to feed all five penguins for 60 days?
- A penguin egg/food ratio is calculated for each penguin as follows. If a penguin laid 10 eggs per day and ate 4 loads of Penguin fodder in 60 days, its egg/food ratio would be 10:4 (or 5:2 in its simplest form).
| Blotwell | Super | Selwyn | Kite | Herodotus | |
Blotwell | × | 12 | 20 | 10 | 15 |
Super | 12 | × | 10 | 62/3 | 84/7 |
Selwyn | 20 | 10 | × | 84/7 | 12 |
Kite | 10 | 62/3 | 84/7 | × | 71/2 |
Herodotus | 15 | 84/7 | 12 | 71/2 | × |
For five penguins the following facts are known:
- Each penguin produces a fixed number of eggs per day, between 1 and 10 inclusive.
- Each penguin has a different egg/food ratio.
- When in its simplest form each egg/food ratio involves two of the numbers 1, 2 and 3.
- The only two penguins producing the same number of eggs per day are Super and Herodotus.
- Selwyn lays more than four eggs per day and has the best egg/food ratio.
Find the total number of eggs the penguins lay in 60 days.
