### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Calendar Capers

Choose any three by three square of dates on a calendar page...

### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

# River Crossing

### The fox, the hen and the corn

Once upon a time a farmer went to market and bought a foxa hen and a sack of corn.

The farmer came to a river which needed to be crossed by boat. He could take only one of his purchases - the fox, or the hen, or the sack of corn - in the boat at a time.

If left together on the riverbank, the fox would eat the hen, or the hen would eat the corn.

Can you find a way for the farmer to get all of them across the river safely?

Two adults and two children need to cross a river in a rowing boat. Can you determine how to get everyone across, and how many crossings are needed, given the following information?
• All adults weigh the same
• Each child weighs half as much as an adult
• The boat can only carry the weight of one adult
• The boat must have someone in it to row it!
What if there were $4$ adults and $2$ children?
What if there were $100$ adults and $2$ children?
What if there were $n$ adults and $2$ children?

If you enjoyed these problems, you may also like to take a look at Crossing the Bridge.

With thanks to Don Steward, whose ideas formed the basis of this problem.

Notes and Background

When you try to solve these 'river crossing' puzzles, you are attempting some of the same problems that were set by Alcuin, an ecclesiastic from the 9th century, for the Emperor Charlemagne.

Alcuin's version of Problem 1 concerned a wolf, a goat and a cabbage.