TMUA 2017 Paper 2 Q20 — Worked Solution

P2·Logic & Quantifiers, Sets & Counting·6.5Official · 2017 · Q20

password-puzzleconstraint-satisfactiondecision-tree

I have forgotten my 5-character computer password, but I know that it consists of the letters

a

b

c

d

e

in some order.When I enter a potential password into the computer, it tells me exactly how many of the letters are in the correct position.When I enter

abcde

, it tells me that none of the letters are in the correct position. The same happens when I enter

cdbea

and

eadbc

.Using the best strategy, how many further attempts must I make in order to guarantee that I can deduce the correct password?

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TMUA 2017 Paper 2 Question 20

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