MathDB

27

Part of 2002 National Olympiad First Round

Problems(1)

P27 [Combinatorics] - Turkish NMO 1st Round - 2002

Source:

8/11/2014
The keys of a safe with five locks are cloned and distributed among eight people such that any of five of eight people can open the safe. What is the least total number of keys?
<spanclass=′latex−bold′>a)</span> 18<spanclass=′latex−bold′>b)</span> 20<spanclass=′latex−bold′>c)</span> 22<spanclass=′latex−bold′>d)</span> 24<spanclass=′latex−bold′>e)</span> 25 <span class='latex-bold'>a)</span>\ 18 \qquad<span class='latex-bold'>b)</span>\ 20 \qquad<span class='latex-bold'>c)</span>\ 22 \qquad<span class='latex-bold'>d)</span>\ 24 \qquad<span class='latex-bold'>e)</span>\ 25