How many gamma-rays from the burst strike the detector per hour?

12,3340

Ignoring relativistic effects and the fact that GRBs do NOT emit isotropically (but rather in collimated jets) you can draw a big sphere around your star, 10 billion light years in radius, and find out what percentage of the surface area of that sphere is a 1 square meter detection array orbiting Earth.  Then you need to determine, using E = Planck's constant x frequency, how many 250 KeV photons are emitted by the GRB, then multiply it by the ratio of the detector array surface area to the surface area of a 10 billion light year sphere.