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checkbox formula fields

I have six checkboxes in an event that where each one represents a certain stage of a demo/webinar. As the salesperson checks off the boxes for stages of the demo they have completed I would like to have a forumal field display whether or not the demo is completed which is based on a certain number of checkboxes being checked. Basically if any 3 of the first 5 checkboxes are checked, the demo is a "completed demo" or if the last checkbox is selected regardless of the other checkboxes being selected, the demo is completed.

for example:
s1 + s3 + s4 = completed demo
s1 + s6 = completed demo
s1 + s3 = not completed
We have a series of 4 checkboxes that we wanted to use to create a code.  We found there were quite a number of combinations required and when using IF we had to have a statement to check each of the boxes for checked or not checked status for every combination possible (if you are a math person the total possible would have been greater if we cared about the order but we did not).
For example the first line checks if Key is checked and Target, Popular, and Redone are not checked, then the code is set to K.
It gets kind of tedious (it amounts to 13 nested IF statements)  and actually did not work until the character limit was recently increased, so with six checkboxes you have your work cut out for you.  I found it helpful top layout the combinations in a spreadsheet and built the formula in notepad and brought it into Salesforce using a lot of trial and error.  This should give you a good place to start.
IF(AND(Target__c,AND(NOT(Key__c), NOT(Popular__c),NOT(Redone__c))),"T",
IF(AND(Popular__c,AND(NOT(Key__c),NOT( Target__c),NOT(Redone__c))),"P",
IF(AND(Redone__c,AND(NOT(Key__c),NOT (Target__c),NOT(Popular__c))),"R",
IF(AND( Key__c,Target__c, Popular__c, Redone__c),"KTPR",
IF(AND( Key__c,Popular__c,AND(NOT(Target__c),NOT(Redone__c))),"KP",
IF(AND( Key__c,Popular__c, Redone__c,AND(NOT(Target__c))),"KPR",
IF(AND( Key__c, Redone__c,AND(NOT(Target__c),NOT(Popular__c))),"KR",
IF(AND( Target__c, Popular__c,AND(NOT(Key__c),NOT(Redone__c))),"TP",
IF(AND( Target__c, Popular__c, Redone__c,AND (NOT(Key__c))),"TPR",
IF(AND( Popular__c, Redone__c,AND(NOT(Key__c),NOT(Target__c))),"PR",
hahah, i was afraid that this was the truth. regardless, thank you for the response, ill give it a shot