# GeekDad Puzzle of the Week: Captain Danger and the Spheres of Death – Solution

Congratulations to Chris Schlanger, who increased Captain Danger’s odds of commuting his sentence correctly and increased his chances of receiving a \$50 code to ThinkGeek to 100%! Check the solution after the jump to receive your code for \$10 off of your next ThinkGeek purchase of \$40 or more.

Special thanks to ThinkGeek for providing our prizes!

Captain Dirk Danger of the Starsystem Quantum Action Team (S.Q.A.T.)
and his first mate have been captured by the dreaded Zorn. As is the
Zorn way, they have presented our heroes with a chance to commute their death sentence. The prisoners are presented with two large vessels. One is filled with fifty black spheres, the other with fifty white spheres.
The chief executioner will draw randomly from one of the two vessels.
If the sphere is black, it is death. If it is white, it is life of hard labor on the prison planet of Exar.

The night before their sentence, Captain Danger and his mate devise a clever plan. They might be able to help their situation by mixing up the spheres in each vessel. There is nowhere to dispose of the spheres, so eliminating the black spheres is impossible. Plus, the Zorn are intelligent so their plan must keep the same number of spheres yet increase their chances as much as possible. They could mix up the spheres so that there were twenty-five of each color in each vessel, making sure the white spheres were on top. But the executioner might shake the vessels, or reach to the bottom and pull a sphere.

Suddenly, it occurs to Captain Danger that there is another way to help themselves.

How does Captain Danger and his mate help their situation?

SOLUTION

Captain Danger moves all of the spheres except one white into one vessel. There is a 50/50 chance that the Zorn executioner will select the vessel with the single white sphere. In the other vessel, there is a 49/99 chance of selecting a white sphere. The combined net chance of survival on, and thereby potential escape from, the prison planet of Exar is a little under 75%.

Coupon code PUZZLING will get \$10 off of your next purchase of \$40 or more at ThinkGeek!