Grade 9 MathGrade 9 Math

Problem of the WeekProblem of the Week

Week #1 (Sept 21)Week #1 (Sept 21)

How long will it take a mile-long train going How long will it take a mile-long train going 20 miles per hour to get completely through 20 miles per hour to get completely through a 2-mile-long tunnel?a 2-mile-long tunnel?

Solution Week #2Solution Week #2

9 minutes. If the train is going 20 mph, it will 9 minutes. If the train is going 20 mph, it will travel 1 mile in 3 minutes. It will take the travel 1 mile in 3 minutes. It will take the engine 6 minutes to go through the tunnel, engine 6 minutes to go through the tunnel, but it will take another 3 minutes for the but it will take another 3 minutes for the caboose to go 1 mile to clear the tunnel.caboose to go 1 mile to clear the tunnel.

Week 1 (Sept 18)Week 1 (Sept 18)

A school has a hall with 500 lockers, all of which A school has a hall with 500 lockers, all of which are closed. Five hundred students start down the are closed. Five hundred students start down the hall. The first student opens every locker. The hall. The first student opens every locker. The second student closes all the lockers that are second student closes all the lockers that are multiples of 2. The third student changes (closes multiples of 2. The third student changes (closes an open locker or opens a closed one) all an open locker or opens a closed one) all multiples of 3. The fourth student changes all multiples of 3. The fourth student changes all multiples of 4, and so on. After all students have multiples of 4, and so on. After all students have finished with the lockers, which numbered lockers finished with the lockers, which numbered lockers will be open? Describe the pattern. will be open? Describe the pattern.

Solution Week #1Solution Week #1

11. 11. Lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, Lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169,

196, 225, 256, 289, 324, 361, 400, 441, and 484 will be 196, 225, 256, 289, 324, 361, 400, 441, and 484 will be open. The pattern is that all locker numbers that are perfect open. The pattern is that all locker numbers that are perfect squares will be open after all students pass. Using the squares will be open after all students pass. Using the strategy for problem number 6, the pattern indicates that all strategy for problem number 6, the pattern indicates that all perfect squares less than or equal to 500 will be open after perfect squares less than or equal to 500 will be open after all students pass. Trial and error show that 232 = 529, all students pass. Trial and error show that 232 = 529, whereas 222 = 484. Therefore, 22 lockers will be open, the whereas 222 = 484. Therefore, 22 lockers will be open, the squares of the numbers 1–22, which are 1, 4, 9, 16, 25, 36, squares of the numbers 1–22, which are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, and 484. 361, 400, 441, and 484.

Week #3 (Oct 1)Week #3 (Oct 1)

A princess is in love with a dashing knight. A princess is in love with a dashing knight. Unfortunately, the king prefers another Unfortunately, the king prefers another suitor for his daughter. The king has locked suitor for his daughter. The king has locked her in the castle’s tower. The castle is her in the castle’s tower. The castle is surrounded by a moat that is 10 yards wide. surrounded by a moat that is 10 yards wide. The knight wants to cross the moat, but he The knight wants to cross the moat, but he has only two 9.75 yard planks and no way to has only two 9.75 yard planks and no way to fasten them together. How can the brave fasten them together. How can the brave knight bridge the moat? knight bridge the moat?

Week (Oct 15)Week (Oct 15)

How much money would you make in 8 How much money would you make in 8 days if you made 8 dollars every time the days if you made 8 dollars every time the hands of a clock formed a 90 degree angle? hands of a clock formed a 90 degree angle?

Week 4 (Oct )Week 4 (Oct )

If A = 1, B = 2, C = 3, . . . , and Z = 26, find If A = 1, B = 2, C = 3, . . . , and Z = 26, find the spelling of a particular quadrilateral the spelling of a particular quadrilateral whose letters are all different and will sum to whose letters are all different and will sum to 114. 114.

Week 5 (October 1)Week 5 (October 1)

““We need more boys in the club,” said Maryanne. We need more boys in the club,” said Maryanne. “Why?” asked Patty. “Well, we have 32 members “Why?” asked Patty. “Well, we have 32 members now, and only 1/4 are boys,” Maryanne explained. now, and only 1/4 are boys,” Maryanne explained. “That’s not too good,” Patty admitted. “You’re “That’s not too good,” Patty admitted. “You’re right,” said Maryanne. “We have to get some more right,” said Maryanne. “We have to get some more boys to join. At least 1/3 of the members must be boys to join. At least 1/3 of the members must be boys.” “That would be a more balanced club,” boys.” “That would be a more balanced club,” Patty agreed. How many more boys would they Patty agreed. How many more boys would they need if no more girls joined their club? need if no more girls joined their club?

Week 6 (October 23)Week 6 (October 23)

What is the 99th letter in the pattern What is the 99th letter in the pattern ABBCCCDDDD . . . ABBCCCDDDD . . .

Week 7 (October 30)Week 7 (October 30)

How many triangles are in the figure below? How many triangles are in the figure below?