The Instant Challenge (or Spontaneous Problem in Odyssey terminology) is described well on the DI web site: http://www.idodi.org/index.php/2009-10-season/instant-challenges
Instant Challenges require teams to engage in quick critical thinking. At a Tournament, a team will receive an Instant Challenge and the materials with which to solve it. The team members must think on their feet by applying appropriate skills to produce a solution in a period of just five to eight minutes. While Team Challenges build long-term problem solving and teamwork skills, Instant Challenges provide an exciting, impromptu creative experience for competing teams. By practicing Instant Challenges during the course of the season, students can increase their improvisational skills and train their minds to work quickly!
On the right hand side of the Instant Challenges web site are some examples you can view.
Two of my favorites from Odyssey are:
30 pieces of linguine
1/2 cup of mini marshmallows (or a 1 inch cube of modeling clay)
Build a structure that hangs out over the edge of a table. Give a point for every inch.
A variation of this is: Build a structure that holds a container at least 5 inches off the ground. Give a point for every weight that the raised container holds. Use nails or pennies for the weights.
Select an object or set of objects (e.g. chop sticks) and pass them around. Each team member says, "This may look like a X, but it is really a Y." For example, the first person would say, "This may look like chop sticks, but it is really walrus tusks" and hold the chop sticks to their mouth to show walrus tusks. The next team member would say, "This may look like walrus tusks, but it is really antenna" and hold the chop sticks to the top of their head. Get it?
Finally, typing "destination imagination instant challenges" into google gives lots of sites with lots of ideas.