clarification on 45-day replacement property

[Vlad Selsky]

Next year my parents plan to sell two of their rental condos and exchange for a single family home that they will rent out to me. I have a question on the 45-day replacement properties. Are my parents obligated to only buy one of those 3 properties? 

1) Say it is day 50 and we failed to buy the homes. Can we continue to search for other properties and complete the exchange?
2) If not, say it is day 30 and we failed to buy the homes. Can we continue to search for other properties up to day 45?