Desmond and Lennon have some cards each. If Lennon gives Desmond 56 cards, they will have an equal number of cards. If Desmond gives Lennon 166 cards, the ratio of the number of cards Lennon has to the number of cards Desmond has would be 13:1. How many cards does Desmond have at first?
Let x be the number of cards Desmond has. Then Lennon has x+56 cards.
If Desmond gives Lennon 166 cards, Lennon will have x+56+166=(x+222) cards.
The ratio of the number of cards Lennon has to the number of cards Desmond has is (x+222):x=13:1.
Thus, (x+222)/x=13/1
x+222=13x
222=12x
x=<<18=18>>18 cards. Answer: \boxed{18}.
Let's assume that Desmond has x cards at first.
According to the statement, if Lennon gives Desmond 56 cards, they will have an equal number of cards.
So, after Lennon gives Desmond 56 cards, Desmond will have x + 56 cards and Lennon will have x cards.
Now, if Desmond gives Lennon 166 cards, the ratio of the number of cards Lennon has to the number of cards Desmond has would be 13:1.
Therefore, we can write the equation:
(x - 166) / (x + 56) = 13 / 1
By cross multiplication, we get:
13(x + 56) = x - 166
Expanding the equation:
13x + 728 = x - 166
Moving x to the left side:
13x - x = -166 - 728
12x = -894
Dividing both sides by 12:
x = -894 / 12
x = -74.5
Since the number of cards cannot be negative or a decimal, it means that our assumption is incorrect.
Therefore, Desmond cannot have -74.5 cards.
Hence, there seems to be no valid solution to this problem. Please cross-check the given information or rephrase the question.