There are 150 'zeroes' and 151 'ones' written on a black board. A step involves choosing three digits and replacing them with a single digit. If all the three digits are identical, they are replaced with the same digit. Otherwise, the digit that appears twice replaces the three chosen digits. What is the minimum number of steps after which there will be no zero written on the blackboard?
Pick:
A) 11
B) 37
C) 36
D) 76
E) 33
If we strike out 3 zeros, we are in effect reducing two zeroes. So we need 74 steps to reduce 148 zeroes. There are 2 zeroes and 151 ones left now. The remaining zeroes can be reduced in 2 steps. Hence the answer is 76.   Answer:76
<result>D</result>
There are 150 'zeroes' and 151 'ones' written on a black board. A step involves choosing three digits and replacing them with a single digit. If all the three digits are identical, they are replaced with the same digit. Otherwise, the digit that appears twice replaces the three chosen digits. What is the minimum number of steps after which there will be no zero written on the blackboard?