How does Jem realize that Boo Radley was the one who placed a blanket on Scout's shoulders during the fire?

In chapter 8 of To Kill a Mockingbird, on the coldest night in Atticus's memory, Atticus wakes the children in the middle of the night because Miss Maudie's house is on fire. Scout and Jem are told to stand out of the way near the Radley place. The children stay where they've been told and watch as the neighbors work to save some of Miss Maudie's belongings from the burning house. Scout notices how the men have shed their robes due to the heat of the flames, but she is cold.
Once the fire is extinguished and they are back in their own house, Atticus notices something about Scout and states, "I thought I told you two to stay put." The children explain that they stayed in front of the Radley place as they were told. Atticus then asks, "Then whose blanket is that?" Scout then becomes aware of the blanket across her shoulders.
As Jem is remembering the events, he recalls that Mr. Radley was fighting the fire with the other men, which means he could not have been the one to cover Scout with the blanket. Since all of the other men were seen near the fire, Jem arrives at the conclusion that Boo Radley must have been the one to place the blanket around Scout. Scout is so consumed with watching the fire that she doesn't notice.