If he arranges the chairs and six years of the same morning he has all the chairs left over if he arranges the chairs and four rows of the same link he has 19 years left over how many chairs does Liam have

6 years of the same morning?

To find the number of chairs Liam has, we can set up a system of equations based on the information given.

Let's denote the number of chairs Liam has as "x".

According to the first statement, if he arranges the chairs in six rows, he has some chairs left over. In other words, x is not divisible evenly by 6. We can write this as an equation: x ≡ k (mod 6), where k is the number of chairs left over after dividing x by 6.

According to the second statement, if he arranges the chairs in four rows, he has 19 chairs left over. We can write this as another equation: x ≡ 19 (mod 4).

Now, we can solve this system of equations to find the value of x.

One approach is to find a common solution to both congruences using the Chinese Remainder Theorem (CRT).

The Chinese Remainder Theorem states that if we have a system of congruences in the form:
x ≡ a (mod m₁)
x ≡ b (mod m₂)
...
x ≡ n (mod mₙ)

where m₁, m₂, ..., mₙ are pairwise coprime (i.e., their greatest common divisor is 1), then there exists a unique solution for x modulo M, where M = m₁ * m₂ * ... * mₙ.

In our case, the congruences are:
x ≡ k (mod 6)
x ≡ 19 (mod 4)

Since 6 and 4 are not pairwise coprime (their greatest common divisor is 2), we need to modify the congruences to make them pairwise coprime.

To do this, we can find a new value for k that satisfies both congruences. We need to find a value of k such that:
k ≡ 19 (mod 4), and
k ≡ m (mod 6), where m is some value.

Since 19 ≡ 3 (mod 4), we can substitute k = 3 into the second congruence:
3 ≡ m (mod 6)

Solving this congruence, we find that m = 3 or m = 9 (since 3 ≡ 3 (mod 6) and 9 ≡ 3 (mod 6)).

Therefore, we have two modified congruences:
x ≡ 3 (mod 6)
x ≡ 19 (mod 4)

Now, these congruences are pairwise coprime, so we can solve them using the Chinese Remainder Theorem.

The solution x modulo M (where M = 6 * 4 = 24) is the common solution to both congruences.

Using the Chinese Remainder Theorem, we obtain:
x ≡ (3 * 4 * 15 + 19 * 6 * 1) % 24
x ≡ (180 + 114) % 24
x ≡ 294 % 24
x ≡ 6 (mod 24)

Therefore, Liam has 6 chairs.

I'm sorry, but I didn't understand your question. Could you please rephrase it or provide more information?