Problem: Eta Carinae is the most prominent variable star in Carina; with a mass of approximately 100 solar masses and 4 million times as bright as the Sun. It was first discovered to be unusual in 1677, when its magnitude suddenly rose to 4, attracting the attention of Edmond Halley. Eta Carinae is inside NGC 3372, commonly called the Carina Nebula. It had a long outburst in 1827, when it brightened to magnitude 1, only fading to magnitude 1.5 in 1828. Its most prominent outburst made Eta Carinae the equal of Sirius; it brightened to magnitude −1.5 in 1843. However, since 1843, Eta Carinae has remained relatively placid, having a magnitude between 6.5 and 7.9. However, in 1998, it brightened again, though only to magnitude 5.0, a far less drastic outburst. Eta Carinae is a binary star, with a companion that has a period of 5.5 years; the two stars are surrounded by the Homunculus Nebula, which is composed of gas that was ejected in 1843.

How many years after Eta Carinae was first discovered to be unusual did it brighten to magnitude −1.5?
Answer: 166

Problem: The Raiders opened the scoring on their first drive of the game, settling for a field goal to take a 3-0 lead.  The Browns failed to score and trailed 3-0 after the first quarter. The Raiders scored a second quarter touchdown to take a 10-0 lead.  Late in the half, the Browns reached the Raiders' 1 yard line and had 1st and goal at the 1.  However, they failed to get into the end zone in three attempts.  After a false start penalty on 4th and goal, the Browns settled for a field goal to cut the deficit to 10-3.  With less than 2 minutes remaining in the half, the Raiders drove down the field, and QB Derek Carr threw a touchdown pass, giving the Raiders a 17-3 lead at halftime.  Early in the third quarter, the Raiders kicked another field goal and went up 20-3.  The Browns finally reached the end zone in the third quarter as QB Josh McCown completed a 28-yard pass to TE Gary Barnidge, cutting it to 20-10.  The Raiders scored another touchdown early in the 4th quarter, and the Browns trailed 27-10.  At that moment, the Browns began to mount a 4th quarter rally.  K Travis Coons kicked a field goal to pull within 27-13.  The Raiders turned the ball over in their own territory on their next drive, and the Browns scored another touchdown to cut the deficit to 27-20.  The Browns' defense forced a 3 and out, and the Raiders were forced to punt.  However, Travis Benjamin muffed the punt, and the Raiders recovered it.  The Raiders ran three more plays before they punted again, pinning the Browns at their own 2 yard line.  The Browns had one last chance to score a game saving touchdown.  Within 2 minutes, they reached the Raiders' 29 yard line.  After McCown was sacked, the Browns faced 3rd and 14 on the Raiders' 34 yard line with under 45 seconds to play.  At that moment, McCown threw a pass that was intercepted by Charles Woodson.  With no timeouts remaining, the Raiders were able to kneel and run out the clock.

How many points were scored in the first half of the game?
Answer: 20

Problem: The Bills opened the regular season on the road against the first of their three divisional rivals, the New England Patriots and got off to a fast start, as on the very first play, Takeo Spikes sacked Tom Brady, causing a fumble recovered by London Fletcher-Baker for a 5-yard TD. The Patriots tied the game up at 7-7 on a 9-yard pass from Brady to Troy Brown. The Bills would regain the lead on a 53-yard FG by Rian Lindell. In the second quarter, Anthony Thomas would make the score 17-7 at halftime with an 18-yard run. However, the Bills continued their late-game struggles from 2005, as they gave up 12 unanswered points in the second-half (a 17-yard pass from Brady to Kevin Faulk, a32-yard FG by Stephen Gostkowski and a safety by Ty Warren with 8:33 remaining in the fourth-quarter), dropping the Bills to 0-1 to start the season.

How many second quarter touchdowns did Tom Brady throw?
Answer: 1

Problem: In 1700, Charles XII had a standing army of 77,000 men . By 1707 this number had swollen to at least 120,000 despite casualties. Russia was able to mobilize a larger army but could not put all of it into action simultaneously. The Russian mobilization system was ineffective and the expanding nation needed to be defended in many locations. A grand mobilization covering Russia's vast territories would have been unrealistic. Peter I tried to raise his army's morale to Swedish levels. Denmark contributed 20,000 men in their invasion of Holstein-Gottorp and more on other fronts. Poland and Saxony together could mobilize at least 100,000 men.

How many more men were with Poland and Saxony than with Denmark?
Answer:
80000