Bubble Monsters

Will the children make it safely through the bubble monsters?

Several children are lined up as a team facing the fearsome bubble monsters. The children aim to make their way safely through all the bubble monsters to the right, while the monsters aim to block them.

The game proceeds in a sequence of moves. On each move, the children appoint one amongst them to poke through the particular bubble monster that blocks them. Thankfully, the child will succeed in getting through, but with the worrisome result that the bubble monster, as his discretion, may possibly divide itself into one or more newly formed bubble monsters behind the child, an arbitrary number of duplicates chosen by the monster.

Perhaps the game proceeds as follows:

The first child successfully passed through the leading monster, which duplicated into three, for a total of five monsters. Then the next child poked through her monster, which regenerated as four, for a total of eight monsters. Oh dear, the monster problem is getting worse! The children face a difficult realization of their precarious position—the only way for them to reach safety, after all, is to push through the monsters, but whenever they do so, additional monsters are created in the wake, which must still be surmounted.

Is it hopeless? How can the children possibly succeed? Can we save any of the children? How many can we save? By what procedure shall they proceed? Should they try to stay together somehow as a group? Or will it be better for at least some of them to charge straight ahead?

Interlude

This game continues my series of posts on interesting sequence games, beginning last time with Face Up. Next time we’ll have the games Pushpast and Pushthrough.

Today, we’ll give a complete analysis of the Bubble Monster game. Enjoy!