$.$ A sadistic guard neatly lines up his $100$ prisoners in height order, prisoner P$0$ the tallest, prisoner

P$99$ the shortest, with each prisoner Pi facing the back of prisoner Pi $+1.($The guard, having

majored in CS$,$ prefers to index his prisoners starting at $0.)$ So situated, prisoner Pi can see the

head of each prisoner Pj with j $>$ i$.$ The guard shouts: $$I shall now place hats atop your stupid

little heads. Either a black hat or a white hat. Then I shall ask you, starting at prisoner P$0$ and

moving my way to prisoner P$99,$ if your own hat is black or is white. Shout it out. If you answer

correctly, you will live another day. If you answer incorrectly, I will shoot you without delay. Bang!

If you try to communicate with one another once our game begins, I will shoot you all.$$

The prisoners briefly confer and agree to a strategy to minimize their losses. Describe it$.$

Hint: Think parity$/$XOR$.$