How To Count Matches Between Two Tables?

Hello. I'm quite new to SQL so have included as many details as i can think of here. The scenario is a wordsearch style puzzle. The user can select their answers in any order and these answers are stored in a table. I need help with the UPDATE statement to compare the users answers against the correct answers for that puzzle.
(Note: In the actual scenario there will be 10-15 answers per grid, but i have reduced the number to make testing easier - hopefully the code for a working UPDATE statement will be scalable to account for grids with different numbers of answers etc.)

The Tables:
-- These are the correct answers for a given grid (gridid).
-- Due to the nature of the puzzle, answers can be in any order.
-- Each level may contain one,two,or no 'bonusanswers' which are harder to find, so these are scored separately so bonus points can be awarded.
CREATE TABLE correctanswers
(
gridid smallint IDENTITY(1,1)PRIMARY KEY CLUSTERED,
answer1 char(15),
answer2 char(15),
bonusanswer1 char(15),
bonusanswer2 char(15)
)

-- These are the user submitted set of answers 'answerid' for level 'gridid'.
-- Answers may be submitted in any order.
CREATE TABLE useranswers
(
answerid smallint IDENTITY(1,1)PRIMARY KEY CLUSTERED,
gridid smallint,
firstanswer char(15),
secondanswer char(15),
thirdanswer char(15),
fourthanswer char(15),
)

-- A user (userid) submits their answers which get stored as answerid.
-- This table shows the scores for each set of answerid's the user has submitted.
-- A high score table for both the individual user, and all users may be created using this table.
CREATE TABLE userscores
(
userid smallint,
answerid smallint,
mainmatches smallint,
bonusmatches smallint
)

The Test Data:
-- sample test data
-- 2 users userid's '1' and '2' each have two goes on level1 (gridid 1)

-- correct answers for gridid 1
INSERT INTO correctanswers (answer1, answer2, bonusanswer1, bonusanswer2) VALUES ('cat','dog','rabbit','elephant')

-- user submitted answers for gridid 1
INSERT INTO useranswers (gridid, firstanswer, secondanswer, thirdanswer, fourthanswer) VALUES (1,'dog','rabbit','horse','cow')
INSERT INTO useranswers (gridid, firstanswer, secondanswer, thirdanswer, fourthanswer) VALUES (1,'dog','cat','elephant','horse')
INSERT INTO useranswers (gridid, firstanswer, secondanswer, thirdanswer, fourthanswer) VALUES (1,'rabbit','cat','elephant','donkey')
INSERT INTO useranswers (gridid, firstanswer, secondanswer, thirdanswer, fourthanswer) VALUES (1,'horse','cat','dog','sheep')

-- scores for users attempts - columns 3 and 4 needs calculating
INSERT INTO userscores VALUES (1,1,null,null) -- one main answer and one bonus answer, so null,null should be 1,1
INSERT INTO userscores VALUES (1,2,null,null) -- two main answers and one bonus answer, so null,null should be 2,1
INSERT INTO userscores VALUES (2,3,null,null) -- one main answer and two bonus answers, so null,null should be 1,2
INSERT INTO userscores VALUES (2,4,null,null) -- two main answers and no bonus answers, so null,null should be 2,0

I have included the correct new table values for the sample data - basically filling in the two null fields in the 'userscores' table.

I haven't used SQL much but from the little i know then i think the answer will include JOIN, COUNT and IN statements as part of the UPDATE statement...but i haven't a clue where to start with the order/logic etc.

I have looked for sample solutions myself but all the examples i have found so far are to do with exact matches between two tables, whereas in my scenario i need to know how many matches, irrelevant of the order.


Many thanks.
Roger