Why did Sichon refuse Yisrael's request to pass through his land?
Rashi: Because all the kings of Cana'an paid him a tax to protect them against invading armies. 1
What prompted Sichon to leave his fortified towns to attack Yisrael in the open?
Rashi: Hakadosh-Baruch-Hu put into the heads of all the soldiers to gather in one location and to attack Yisrael from one location.
Why did Hashem induce Sichon and his army to leave their towns and their country and attack Yisrael in the desert?
Rashi: a. To spare Yisrael the trouble of besieging each city indepently. Now, they killed the men, and went from there to capture their towns. 1 b. Miracles aside, Sichon's city was impregnable, even if it would have been inhabited by mosquitoes; 2 and Sichon was invincible, even if he would be in an open village.
Oznayim la'Torah: Because, had they fought inside their country, a. they would have been able to flee to their towns, making it more difficult to subsequently capture them; b. fighting inside the country would have caused the land - which Yisrael were destined to conquer - to become devastated, whereas now they took over the cities intact.
Rashi: Which now had only women and children inside.
Are women and children less than mosquitoes? (When Sichon's army left town to attack Yisrael, they left the gates open). The Meraglim were stunned at the strength of a Cana'ani girl. Refer to 13:28:151:1 (PF)