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23

Part of 1999 National Olympiad First Round

Problems(1)

Turkish NMO First Round - 1999 P-23 (Combinatorics)

Source:

7/3/2012
Hour part of a defective digital watch displays only the numbers from 11 to 1212. After one minute from n:59 n: 59, although it must display \left(n \plus{} 1\right): 00, it displays 2n:00 2n: 00 (Think in mod 12 mod\, 12). For example, after 7:59 7: 59, it displays 2:00 2: 00 instead of 8:00 8: 00. If we set the watch to an arbitrary time, what is the probability that hour part displays 44 after exactly one day?
<spanclass=′latex−bold′>(A)</span> 112<spanclass=′latex−bold′>(B)</span> 14<spanclass=′latex−bold′>(C)</span> 13<spanclass=′latex−bold′>(D)</span> 12<spanclass=′latex−bold′>(E)</span> None<span class='latex-bold'>(A)</span>\ \frac {1}{12} \qquad<span class='latex-bold'>(B)</span>\ \frac {1}{4} \qquad<span class='latex-bold'>(C)</span>\ \frac {1}{3} \qquad<span class='latex-bold'>(D)</span>\ \frac {1}{2} \qquad<span class='latex-bold'>(E)</span>\ \text{None}
probability