* I will post* seven new problems every weekend, one for each day of the week. The idea is that you work on your own during the week and I will post answers the following Saturday. For those of you who practiced with me last year, the process is similar.

* For instructions* on submitting weekly answers, click on the “Logistics” tab.

*posted problems, click on the “Archive” tab.*

**For previously****, click on the “News” tab.**

*For previous prizes*

**Happy New Year!**

**Week of Jan 13 – Jan 19.**

Click GoogleForm to submit answers by Sat, Jan 19.

Jan 13: In Mr. D’s class, 1/5 of the students failed the math test. Of the remaining students, 1/4 scored an A. What fraction of the students passed the test, but did not score an A?

Jan 14: John is 14 and his mom is 41. Their ages have the same 2 digits. The next time that their ages have the same 2 digits, how old is John?

Jan 15: If 8 less than k is 6 more than m, how much bigger is k than m?

Jan 16: Six people can be seated comfortably in a room 6′ by 8′. How many people can be seated comfortably in a room 12′ by 16′?

Jan 17: If 1/4 is greater than m/16 where m is an integer, what is the biggest possible value of m?

Jan 18: Two numbers are in the ratio of 4:5. If the smaller of the two numbers is 16, what is the bigger number?

Jan 19: A local pizza shop has 10 different choices of toppings. What is the number of combinations for 2 toppings?

**Week of Jan 6 – Jan 12.**

Click GoogleForm to submit answers by Sat, Jan 12.

Jan 6: Two sides of a triangle have lengths 7” and 15”. If the third side also has an integral length, what is the longest possible length of the third side?

Answer: 21”

Jan 7: If 3/4 of a job can be done in 15 days, how many days does it take to finish the whole job?

Answer: 20 days

Jan 8: There are 3 contestants in a hot dog eating contest. By the time Al finishes one hot dog, Ben finishes 3 and Carl finishes 2. The contest is over when Ben finishes his 27th hot dog. How many hot dogs do the three people eat altogether?

Answer: Al: 9, Ben: 27, C: 18. So the total is 54.

Jan 9: If 3 people can make 3 widgets in 3 hours, then how many widgets can 25 people make in 3 hours?

Answer: 25 widgets.

Jan 10: John gives 1/2 of his marbles to Marty, 1/4 of his collection to Norm, 1/6 to Otto and the remaining 30 marbles to Pete. How many marbles does Marty receive?

Answer: Pete gets 1/12 of the marbles, or equivalently 30 marbles. So Marty gets 90 marbles.

Jan 11: A rectangular kitchen floor is 11 ft by 15 ft. Each square tile has perimeter 24 inches. How many tiles are needed to cover the kitchen floor?

Answer: The square tile is 1/2 ft by 1/2 ft. So the kitchen floor needs 4*11*15 = 660 square tiles.

Jan 12: During a track practice, A runs 3/5 of a mile, B runs 4/7 of a mile, C runs 1/2 a mile and D runs 2/3 of a mile. Who runs the farthest?

Answer: D.