# Math

On day one she has to give him one link. There are no choice but cutting 1 link at the end of the chain.

Number of cut: 1 cut.

On day 2, she needs to give him 2 links. She may give him 2 links from the end of the chain and get the link from day 1 back.

Number of cut: 2 cuts.

Chain description: 1 single link, a 2-ring chain, and 20 links chain

Innkeeper possession : 2 chain ring

On day 3 she may give him the link she cut on day 1.

Innkeeper possession : 2 -ring chain, single link

On day 4 she may cut a piece of 4 links at the end of the chain and get the 3 links back from the innkeeper.

Number of cut: 3 cuts.

Chain description: 1 single link, a 2-ring chain, a 4-ring chain, and 16 links chain

Innkeeper possession : 4-ring chain

On day 5,6,7 she is able to pay the right amount with the pieces she has.

On day 8 she cuts a 8-ring piece at the end of the longest chain.

Number of cut: 4 cuts.

Chain description: 1 single link, a 2-ring chain, a 4-ring chain, and 2 8 rings chain

Innkeeper possession : 8-ring chain

On day 9 she may give the single ring

Innkeeper possession : 8-ring chain, 1 single link

On day 10 Innkeeper possession : a 8-ring chain,  a 2-rings chain

On day 11, Innkeeper possession : 8-ring chain, a 2-ring chain and 1 single link

On day 12 Innkeeper possession : 8-ring chain, 4-rings chain

On day 13 Innkeeper possession : 8-ring chain, 4-rings chain, 1 single link

On day 14 Innkeeper possession : 8-ring chain, 4 rings chain, 2-ring chain
On day 15 Innkeeper possession : 8-ring chain, 4 rings chain, 2-ring chain, singe link

On day 16 Innkeeper possession : 2 8-ring chains

On day 17, Innkeeper possession : 2 8-ring chains, single link

On day 18  Innkeeper possession : 2 8-ring chains, 2-ring chain

On day 19 Innkeeper possession : 2 8-ring chains, 2-ring chain, single link

On day 20 Innkeeper possession : 2 8-ring chains, 4 rings chain

On day 21 Innkeeper possession : 2 8-ring chains, 4 rings chain, single link

On day 22, Innkeeper possession : 2 8-ring chains, 4 rings chain, 2-rings chain

On day 23, Innkeeper possession : 2 8-ring chains, 4 rings chain, 2 rings chain single link.

In summary, she managed to pay each day what she owe in 4 cuts. The pieces are 2 8-rings chains,  a 4-rings chain, a 2-rings chain, and a single link.

Approved by eNotes Editorial Team