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Picking the red one<br />
Albie has 200 wooden cubes, half of<br />
them coloured red and the rest painted<br />
in blue. They are otherwise completely<br />
identical, both in shape, weight and surface.<br />
Now he is playing this little game<br />
with one of his crewmates Bertie: Albie<br />
distributes his cubes in two black bags.<br />
Bertie chooses one of the bags and<br />
picks, obviously without looking into<br />
the bags, one wooden cube. If the<br />
cube is blue, Albie pays for the first<br />
round of refreshments at their<br />
next shore leave. Alternatively,<br />
if the cube is red Bertie picks<br />
up the bill.<br />
How should Albie distribute the<br />
cubes to maximise his chances<br />
of winning the game?<br />
I await your suggested solutions by<br />
November 20th 2006 at the very latest.<br />
Good luck!<br />
Solution to Brainteaser 2006Q2<br />
Reaching the boat in Guzzler Bay<br />
In the previous issue the problem was to transport three sailors<br />
over a distance of 75 kilometres in just three hours, only<br />
with the aid of a motorcycle for max two persons with a top<br />
speed of 60 km per hour and by walking at 6 km per hour.<br />
A (Albie) and B (Bertie) start on the motorcycle whilst C (Charlie)<br />
starts walking. At a point z km from the port, B gets off<br />
and continues on foot. The total time spent when arriving at<br />
the boat is the sum of the time spent on the motorcycle and<br />
the time spent walking<br />
tB = (75 - z)/60 + z/6.<br />
As this is less than the total distance of 180 km the motorcycle<br />
is able to drive in 3 hours (3 hours * 60 km per hour), and we<br />
know that B will be able to reach the vessel in time, the three<br />
will reach the boat in time for the departure.<br />
We have only received a handful of solutions this time, but<br />
although the solution approach differs between the suggestions,<br />
at least all the submissions reach the correct answer.<br />
The winner this time is Hans Lund, the former head of the QA<br />
section who now enjoys his retirement in Bergen.<br />
Congratulations, Hans!<br />
This could be max 3 hours, giving that z must be not more<br />
than 11 1 / 3 km.<br />
When A and B reaches the point z km from port, C has been<br />
walking x km. As his speed is one tenth of the motorcycle’s,<br />
x = (75 - 11 1 / 3)/10 = 6 11 / 30 km.<br />
A drives back to pick up C and the two meet after he has been<br />
driving y km back:<br />
y = [75 - 11 1 / 3 - 6 11 / 30] · 10 / 11 = 52 1 / 11<br />
A and C turns around the bike again, and when reaching the<br />
boat the total distance for<br />
A is (75 - z) + 2 * y + z = 75 + 104 2 / 11 = 179 2 / 11<br />
ODFJELL Quarterly September 2006 27
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