Short answers, pulled from the story.
The Battle of the Bulge ran from the 16th of December 1944 to the 25th of January 1945. The German assault began at 05:30 on the 16th of December with a 90-minute artillery barrage along an 80-mile front in the Ardennes region of Belgium and Luxembourg.
Germany aimed to capture the Belgian port of Antwerp and split the Allied lines, trapping four Allied armies without supplies. Hitler hoped this would force the western Allies to negotiate a separate peace independent of the Soviet Union. The plan required reaching the Meuse River by the third day and seizing Antwerp by the fourth.
The Allies considered the Ardennes a quiet sector and underestimated German offensive capability. German forces maintained strict radio silence, used telephone and teleprinter instead of radio inside Germany (reducing Ultra intercepts), and disguised their buildup as defensive preparations. Three American intelligence officers correctly predicted the attack, but their warnings were dismissed by the 12th Army Group.
Brigadier General Anthony McAuliffe, acting commander of the 101st Airborne Division, replied 'NUTS!' to the German demand for Bastogne's surrender on the 22nd of December 1944. Lieutenant Colonel Harry Kinnard noted that McAuliffe's initial off-the-cuff response would be 'tough to beat,' and it was typed up and formally delivered to the German commander.
On the 17th of December 1944, near the hamlet of Baugnez, SS troops of Kampfgruppe Peiper opened fire on approximately 150 American prisoners of war who had surrendered. At least 84 prisoners were murdered. Following the end of the war, soldiers and officers of Kampfgruppe Peiper, including Peiper and SS general Dietrich, were tried for the killings at the Malmedy massacre trial.
German forces suffered between 63,000 and 104,000 men killed, missing, wounded, or captured out of over 410,000 committed. Allied forces, which eventually totaled more than 700,000 men, suffered from 77,000 to more than 83,000 casualties, including at least 8,600 killed. The battle is recorded as the largest and bloodiest single battle fought by the United States in the Second World War.