Query to find 2 cheapest items sum value of which gives 3000 - sql

Question

I have a table Products:
ProductName Price
straight jeans 1500
slim jeans 2500
Denim jacket 3000
Denim shorts 800
Skinny jeans 1700
loose Jeans 2100
mom Jeans 2800
wide jeans 1850
distressed jeans 1100
bootcut jeans 1350
For purchased two different things with a total value of 3000 or more, they give a third as a gift.
I need a SQL query to spend minimum on two things, and take third as the most expensive.
The only thing I've come up with is to go through all possible combinations and find the cheapest combination that over 3000.
WITH Products_sum AS (
SELECT p1.ProductName AS ProductName1, p2.ProductName AS ProductName2, p1.Price + p2.Price AS TotalPrice
FROM products p1
JOIN products p2
ON p1.ProductName < p2.ProductName
)
SELECT top 1 ProductName1, ProductName2, TotalPrice
FROM Products_sum
WHERE TotalPrice >= 3000
order by TotalPrice asc
I'm expecting answer like:
bootcut jeans 1350
Skinny jeans 1700
Denim jacket 3000
But don't know how to do exactly like that.

Answer 1

I continued from where you left it and compose the expected result.
Converted as cte the top pair of products and the most expensive.
Combine the final resultset with union statement.
WITH Products_sum AS (
SELECT p1.ProductName AS ProductName1
, p2.ProductName AS ProductName2
, p1.Price + p2.Price AS TotalPrice
, p1.Price Price1
, p2.Price Price2
FROM products p1
JOIN products p2
ON p1.ProductName < p2.ProductName
),
topProducts as (SELECT top 1 ProductName1, ProductName2, Price1, Price2
FROM Products_sum
WHERE TotalPrice >= 3000
order by TotalPrice asc),
moreExpensive as (
select top 1 ProductName, Price
from products
order by price desc
)
select productName, Price from(
select 1 as pos, ProductName1 ProductName, Price1 Price from topProducts
union
select 2, ProductName2 , Price2 from topProducts
union
select 3, ProductName, Price
from moreExpensive )q
order by pos

Answer 2

SELECT p1.ProductName, p1.Price,
p2.ProductName, p2.Price,
p3.ProductName, p3.Price
FROM Products p1
JOIN Products p2
on p1.ProductName < p2.ProductName
JOIN Products p3
ON p2.ProductName < p3.ProductName AND
p1.Price + p2.Price + p3.Price > 3000
LEFT JOIN Products nonexistent
ON NOT (nonexistent.ProductName IN (p1.ProductName, p2.ProductName, p3.ProductName)) AND
p1.Price + p2.Price + nonexistent.Price > 3000 AND
nonexistent.Price < p3.Price
WHERE nonexistent.ProductName IS NULL
We
select every (p1, p2, p3) tuples
where their name differs
their price is greater than 3000
and there doesn't exist any nonexistent record that would differ from these three, would yield a smaller price with p1 and p2 than p3 but still above 3000