Hakim, Rena, Patrice, and Julius line up for a picture. If Patrice and Hakim do not stand beside each other, in how many different ways can the group line up?

If each of the following numbers is written in standard form, what is the final digit?

a) 9^{32}

b) 12^{33}

In how many different ways can you arrange two identical blue blocks and two identical red blocks in a straight line?

What is the most money you can have in $1 coins, $2 coins, $5 bills, $10 bills, $20 bills, and $50 bills, and still not be able to make change for a $100 bill?

Estimate the percent of the North American population that lives within a day’s drive from your school.

A valuable gold coin that had been stolen was recovered, along with seven counterfeit copies that had been placed in the same box. If the counterfeit coins are all identical and are slightly lighter than the real coin, how can the real coin be found with only two weighings on a balance scale?

The number 12 is the first abundant number, because it is the smallest whole number for which the sum of its factors, not including itself, is greater than itself.

\displaystyle 1 + 2+ 3 + 4+ 6= 16

What are the next three abundant numbers?

Which Canadian province has

a) the most fresh water?

b) the most fresh water per person?

Route 66 was a popular two- lane highway that started in Chicago and ended in Los Angeles. Much of Route 66 still exists, but most travellers now use the superhighways that run parallel to it. The cities on Route 66 include Chicago, Springfield (Illinois), St. Louis, Springfield (Missouri), Tulsa, Oklahoma City, Amarillo, Tucumcari, Albuquerque, Gallup, Flagstaff, Needles, Barstow, and Los Angeles. A newspaper reporter who is writing a story about Route 66 leaves Chicago on May 10 at 08:00. Assume that the reporter drives at 80 km/h for a maximum of 6 h/day and sleeps each night at one of the places on the list. Write an itinerary for the reporter.

There are five courses in the School for the Arts summer program—painting, sculpting, music, drama, and film. Terri can choose three of the courses. In how many different combinations can she choose the three courses?