# Victorboo and Garyboo

**Number Theory**Level 2

Victorboo and Garyboo do push-ups every day. On the first day, as Gary had extraordinary powers of doing push ups, he did 100 push ups. On the second day, Garyboo was tired and he decided to do half the number of push ups. On the third day, Garyboo again did half. On the fourth day, Garyboo realised that even though he may be able to do half, but half would be a decimal. Thus he decided that he should do one less than before. On the fifth day, he did half again. It went on up till Garyboo had only 1 push up to do. Victorboo also decided to do push-ups. He decided to do 150 push ups on the first day. When will he have only 1 push up to do? Notes and Assumptions: If Garyboo reaches 1 push up, he will stop immediately.

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