# Alcuin's Mathematical Puzzles - University of Washington morrow/mathday/... Annie Raymond...

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Alcuins Mathematical Puzzles

Annie Raymond

University of Washington

March 23, 2015

Alcuins problemAlcuin wrote Propositions ad acuendos iuvenes, i.e. problems to sharpenthe young, which contains the following problem:

A man had to transport to the far side of a river a wolf, a goat, and abundle of cabbages. The only boat he could find was one which couldcarry only two of them. For that reason, he sought a plan which wouldenable them all to get to the far side unhurt. Let him, who is able, sayhow it could be possible to transport them safely.

Solution:

The man first brings the goat to the far side and leaves it there.

He goes back and brings the wolf with him, leaving it on the far side,and brings back the goat.

He leaves the goat on the initial side, takes the cabbage and brings itto the far side.

Finally, he goes back to the original shore, and takes the goat to bringit to the far side.

Annie Raymond (University of Washington) Alcuins Mathematical Puzzles March 23, 2015 2 / 13

Alcuins problemAlcuin wrote Propositions ad acuendos iuvenes, i.e. problems to sharpenthe young, which contains the following problem:

A man had to transport to the far side of a river a wolf, a goat, and abundle of cabbages. The only boat he could find was one which couldcarry only two of them. For that reason, he sought a plan which wouldenable them all to get to the far side unhurt. Let him, who is able, sayhow it could be possible to transport them safely.

Solution:

The man first brings the goat to the far side and leaves it there.

He goes back and brings the wolf with him, leaving it on the far side,and brings back the goat.

He leaves the goat on the initial side, takes the cabbage and brings itto the far side.

Finally, he goes back to the original shore, and takes the goat to bringit to the far side.

Annie Raymond (University of Washington) Alcuins Mathematical Puzzles March 23, 2015 2 / 13

Alcuins problemAlcuin wrote Propositions ad acuendos iuvenes, i.e. problems to sharpenthe young, which contains the following problem:

A man had to transport to the far side of a river a wolf, a goat, and abundle of cabbages. The only boat he could find was one which couldcarry only two of them. For that reason, he sought a plan which wouldenable them all to get to the far side unhurt. Let him, who is able, sayhow it could be possible to transport them safely.

Solution:

The man first brings the goat to the far side and leaves it there.

He goes back and brings the wolf with him, leaving it on the far side,and brings back the goat.

He leaves the goat on the initial side, takes the cabbage and brings itto the far side.

Finally, he goes back to the original shore, and takes the goat to bringit to the far side.

Annie Raymond (University of Washington) Alcuins Mathematical Puzzles March 23, 2015 2 / 13

Solution:

The man first brings the goat to the far side and leaves it there.

He goes back and brings the wolf with him, leaving it on the far side,and brings back the goat.

He leaves the goat on the initial side, takes the cabbage and brings itto the far side.

Finally, he goes back to the original shore, and takes the goat to bringit to the far side.

Annie Raymond (University of Washington) Alcuins Mathematical Puzzles March 23, 2015 2 / 13

Solution:

The man first brings the goat to the far side and leaves it there.

He goes back and brings the wolf with him, leaving it on the far side,and brings back the goat.

He leaves the goat on the initial side, takes the cabbage and brings itto the far side.

Finally, he goes back to the original shore, and takes the goat to bringit to the far side.

Annie Raymond (University of Washington) Alcuins Mathematical Puzzles March 23, 2015 2 / 13

Solution:

The man first brings the goat to the far side and leaves it there.

He goes back and brings the wolf with him, leaving it on the far side,and brings back the goat.

He leaves the goat on the initial side, takes the cabbage and brings itto the far side.

Finally, he goes back to the original shore, and takes the goat to bringit to the far side.

Annie Raymond (University of Washington) Alcuins Mathematical Puzzles March 23, 2015 2 / 13

Alcuins modified problem

A man had to transport to the far side of a river a wolf, a goat, a rabbitand a bundle of cabbages. The only boat he could find was one whichcould carry only two of them. For that reason, he sought a plan whichwould enable them all to get to the far side unhurt. Let him, who is able,say how it could be possible to transport them safely.

Anyone?

Clearly impossible! Whatever the man takes first in the boat, there willremain an animal eating something else on the shore.

Lets represent that mathematically!

Annie Raymond (University of Washington) Alcuins Mathematical Puzzles March 23, 2015 3 / 13

Alcuins modified problem

A man had to transport to the far side of a river a wolf, a goat, a rabbitand a bundle of cabbages. The only boat he could find was one whichcould carry only two of them. For that reason, he sought a plan whichwould enable them all to get to the far side unhurt. Let him, who is able,say how it could be possible to transport them safely.

Anyone?

Clearly impossible! Whatever the man takes first in the boat, there willremain an animal eating something else on the shore.

Lets represent that mathematically!

Annie Raymond (University of Washington) Alcuins Mathematical Puzzles March 23, 2015 3 / 13

Alcuins modified problem

A man had to transport to the far side of a river a wolf, a goat, a rabbitand a bundle of cabbages. The only boat he could find was one whichcould carry only two of them. For that reason, he sought a plan whichwould enable them all to get to the far side unhurt. Let him, who is able,say how it could be possible to transport them safely.

Anyone?

Clearly impossible! Whatever the man takes first in the boat, there willremain an animal eating something else on the shore.

Lets represent that mathematically!

Annie Raymond (University of Washington) Alcuins Mathematical Puzzles March 23, 2015 3 / 13

Alcuins modified problem

Anyone?

Lets represent that mathematically!

Annie Raymond (University of Washington) Alcuins Mathematical Puzzles March 23, 2015 3 / 13

Graph representation

We make a graph where each vertex (point) represents ananimal/vegetable/person/thing, and we put an edge between two of themif they cannot be left alone without supervision. We call this graph theAlcuin graph of the problem.

Annie Raymond (University of Washington) Alcuins Mathematical Puzzles March 23, 2015 4 / 13

Graph representation

We make a graph where each vertex (point) represents ananimal/vegetable/person/thing, and we put an edge between two of themif they cannot be left alone without supervision. We call this graph theAlcuin graph of the problem.

Annie Raymond (University of Washington) Alcuins Mathematical Puzzles March 23, 2015 4 / 13

Graph representation

We make a graph where each vertex (point) represents ananimal/vegetable/person/thing, and we put an edge between two of themif they cannot be left alone without supervision. We call this graph theAlcuin graph of the problem.

Annie Raymond (University of Washington) Alcuins Mathematical Puzzles March 23, 2015 4 / 13

Graph representation

Annie Raymond (University of Washingto