I have the following question with me:
"A and B start with p = 1. Then they alternately multiply p by one of the numbers 2 to 9. The winner is the one who first reaches 1000. Who wins : A or B?"
My book tells that A always wins. However, I give steps for B to win in the following way:
Step 1: A multiplies by 2 to give 2.
Step 2: B multiplies by 9 to give 18.
Step 3: A again multiplies by 9 to give 162
Step 4: B again multiplies by 9 to give 1458
Thus crossing 1000 first, B wins the game right. Is this not a possible way in which B can proceed? Is there any problem with my interpretation of my question?