how does a karate player breaks a slab of ice with a single blow?

Your friend have answered correctly but I would like to elaborate it to include behaviour of matter in it. You can easily infer that the same karate master won't be able to break a steel block however hard he blows to it. This happens because every material breaks under a particular pressure (stress) known as breaking stress. 

When a karate player aims at a block of ice or concrete if you observe his hand you will find he chooses a small area of the slab where he plans to strike.  

 He then moves the hand fast and on striking the slab the momentum of his hand becomes zero in a very short time t. F = MV/t, as t is small force F is very large. Now as area A on which he strikes the slab is also very small so pressure F/A becomes very high. This high pressure becomes more than the breaking stress of the ice so it breaks.  

It is also to be noted that an equal and opposite force is also experienced by his hand which could gave broken normal people's hand, but karate players make their bones very strong by constant practices so it endures the high stress.