In December 1944, under overcast skies that limited Allied aerial surveillance, >250,000 German troops and armored divisions launched a surprise attack in the weakly-defended, rugged forest of Ardennes. With a thrust toward Antwerp Belgium, the advance was intended to split the Allied armies in northwest Europe.
Caught completely off guard, reeling American units fought desperate battles to stem the German advance at St.-Vith, Elsenborn Ridge, Houffalize and Bastogne (where the American General Anthony C. McAuliffe replied “nuts” to a German demand for surrender.)
Fierce American resistance on the northern and southern borders of the offensive, blocked German access to key roads needed for success. American resilience, improved flying weather, terrain favorable for defense and shortage of fuel delayed the German advance, allowing the Allies to reinforce their lines and foil the last great German offensive of the war.
Casualties and losses
20,876 Allied soldiers were killed during the Battle of the Bulge, with 42,893 wounded and 23,554 reported captured or missing. German losses totaled 15,652 killed, 41,600 wounded, and 27,582 reported captured or missing.
https://www.life.com/history/battle-of-the-bulge-rare-photos-from-hitlers-last-gamble/