Major Minority Report plot flaw?

(Warning: there are some plot spoilers in this post…you might want to skip it if you haven’t seen the movie yet.)

Reader Adam Z. from Dallas, TX wrote in with something interesting regarding a potential plot problem in Minority Report. Here’s the questionable plot point:

Lamar (played by Max von Sydow) sets up a situation for John (Tom Cruise) to find with the idea that when John enters into this situation (where he’s confronted with evidence of his son’s death), he’ll commit murder. The precogs predict the murder and John sees himself kill an unknown man on the Pre-Crime viewscreens. In the course of trying to clear his good name, John ends up exactly where the precogs predicted and Lamar intended, poised to kill his son’s supposed killer.

Here’s the problem: how did Lamar know that his setup would make the Precogs to predict murder and set the rest of events in motion? As Adam writes, “Cruise only finds the fake killer based on the precogs’ subsequent images of Cruise killing that fake killer, which Sydow could not possibly have known for sure would be shown to Cruise, ever.”

I need to see the movie again to make sure I haven’t missed anything, but I have to agree with Adam on this one…that seems to be a huge hole in the plot. Short of assuming that Lamar tinkered with the precogs to ensure their prediction (which I don’t think he did), there doesn’t seem to be a simple way of resolving this. Does anyone have thoughts about this?