The princes survived
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The prince’s could have easily been hidden away by their family. If they had been killed by Richard in order for him to take the throne, he would have publicly displayed and announced their deaths in order to ensure the public that they were truly gone and wouldn’t cause future problems. Instead, Richard didn’t speak about their disappearance at all. In fact, during Henry VII’s reign in 1495, an army landed at Kent, led by a man claiming to be Richard of York, the younger son of Edward IV . This man claimed that he had three distinctive marks that could prove to anyone who knew Richard Duke of York that it was him. Beyond this, The boys’ mother, Elizabeth Woodville, later left the Westminster sanctuary to join Richard III’s court. Elizabeth also convinced her son not to fight for the rebel cause. If Elizabeth believed that her sons were murdered, she would not have been so eager to rejoin the man who possibly murdered them. Based on the lack of evidence that the boys were murdered, it is entirely likely that they were simply hidden away by their family in order to ensure their safety.
Many people argue that simply because there is no damning evidence that the princes were murdered, that doesn't mean that they survived into Tudor England. Historian Nathan Amin claims that the reason that Richard III kept the deaths of the two princes out of the public was because "If Richard presented the corpses of the princes, just 12 and 9 respectively, to the citizens of London, he would surely have opened himself to accusations of murder at home and abroad. Rumours of their demise were already rife, and the sight of their bodies would have confirmed the suspicions of many". 
Rejecting the premises