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In order to play you need ability, so it's quite natural to say:

(i) I can buy. (ii) I can't buy (Note that we are speaking about the ability to buy, no object is required, sentences (i) and (ii) stand on their own feet.) (iii) I can buy food. (iv) I can buy food with money. (v) I can't buy food without money

1. I have no money. [to do with what?]
2. I have no money with which to buy [to buy what?]
3. I have no money with which to buy food. [outdated]
4. I have no money to buy food with. [the same meaning as 3.]
5. I have no money to buy food. [grammatical]

This is quite formal and some may find it pompous and artificial. Nowadays it is more common to hear:

This construction also holds true in the negative; therefore after the clause I have no friend we can insert with whom before the verb to play as in sentence #2, or we tag the preposition with at the end of the sentence as in #5.

2. *I have no pen to write [for what?]
3. I have no pen to write with

EDIT
In answer to Araucaria's comment “However - I don't understand why to buy food with money is tautological, (i.e. why the ‘with’ is tautological), but to write with a pen is not. In standard British Englishes 4 and 5 are equally acceptable ...”

In order to play a game of soccer you need ability and a ball, so it's quite natural to say:

(i) I can buy. (ii) I can't buy (note that we are speaking about the ability to buy, no object is required, sentences (i) and (ii) stand on their own.) (iii) I can buy food. (iv) I can buy food with money. (v) I can't buy food without money

1. I have no money. [to do with what?]
2. I have no money with which to buy [to buy what?]
3. I have no money with which to buy food. [outdated]
4. I have no money to buy food with. [the same meaning as 3.]
5. I have no money to buy food. [grammatical]

This is quite formal and today's native speakers may find it pompous-sounding and artificial. Nowadays, it is more common to hear:

This construction also holds true in the negative; therefore, after the clause I have no friend we can insert with whom before the verb to play as in sentence #2, or we add the preposition with at the end of the sentence as in #5.

2. *I have no pen to write [to do what?]
3. I have no pen to write with

EDIT
In answer to Araucaria's comment “However - I don't understand why to buy food with money is tautological, (i.e. why the ‘with’ is tautological), but to write with a pen is not. In standard British English, 4 and 5 are equally acceptable ...”

EDIT
In answer to Araucaria's comment “However - I don't understand why to buy food with money is tautological, (i.e. why the ‘with’ is tautological), but to write with a pen is not. In standard British Englishes 4 and 5 are equally acceptable ...”

EDIT
In answer to Araucaria's comment “However - I don't understand why to buy food with money is tautological, (i.e. why the ‘with’ is tautological), but to write with a pen is not. In standard British Englishes 4 and 5 are equally acceptable ...”

EDIT
In answer to Araucaria's comment “However - I don't understand why to buy food with money is tautological, (i.e. why the with is tautological), but to write with a pen is not. In standard British Englishes 4 and 5 are equally acceptable ...”

Why do you think “with money” is not tautological (maybe redundant would have been a better word) to say?

EDIT
In answer to Araucaria's comment “However - I don't understand why to buy food with money is tautological, (i.e. why the ‘with’ is tautological), but to write with a pen is not. In standard British Englishes 4 and 5 are equally acceptable ...”

Why do you think “with money” is not tautological (maybe redundant would have been a better word) to say?