welcome to WebmasterWorld, lennart007!

you can do the front end in html using forms and input elements.

you need server scripting capability to get the form to "do" anything with the input data.
it doesn't have to be php.

you need some form of data storage capability on the server to keep and report on scores and rankings.
a database would be preferable for several reasons.

what kind of server configuration do you have access to?

The server can do anything. Including PHP and databases.

I'd start by checking resources like hotscripts.com, sourcforge, etc., to see if someone has created a script that does what you need. It could be as simple as downloading and installing, with a bit of customization.

Often, a program that has been around for a few versions will have functionality and features that you may not have thought of yet but which could prove useful.

A few programs such as hot potatoes, netquiz, JClick... could help you.

The server can do anything. Including PHP and databases.

my bad - i thought you were asking how to do a quiz without php scripting capability.

try the vanquiz software.