*m*and

*n*are positive integers such that 75

*m*=

*n*

^{3}. What is the minimum possible value of

*m + n*?

Interactive version of problem and solution.

Buy *Hexaflexagons, Probability, Paradoxes, and the Tower of Hanoi* from the MAA Bookstore

Suppose that *m* and *n* are positive integers such that 75*m* = *n*^{3}. What is the minimum possible value of *m + n* ?

Interactive version of problem and solution.

Interactive version of problem and solution.

Buy *Hexaflexagons, Probability, Paradoxes, and the Tower of Hanoi* from the MAA Bookstore

Ali, Bonnie, Carlo and Dianna are going to drive together to a nearby theme park. The car they are using has four seats: one driver's seat, one front passenger seat and two back seats. Bonnie and Carlo are the only two who can drive the car. How many possible seating arrangements are there?

Interactive version of problem and solution.

Interactive version of problem and solution.

Joe and JoAnn each bought 12 ounces of coffee in a 16-ounce cup. Joe drank 2 ounces of his coffee and then added 2 ounces of cream. JoAnn added 2 ounces of cream, stirred the coffee well, and then drank 2 ounces. What is the resulting ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee ?

The positive integers *A, B, A – B,* and *A + B* are all prime numbers. The sum of these four primes is...

(A) even

(B) divisible by 3

(C) divisible by 5

(D) divisible by 7

(E) prime

Interactive version of problem and solution.

(A) even

(B) divisible by 3

(C) divisible by 5

(D) divisible by 7

(E) prime

Interactive version of problem and solution.

Carlos Montado was born on Saturday, November 9, 2002. On what day of the week will Carlos be 706 days old?

Interactive version of problem and solution.

Interactive version of problem and solution.

Bill walks 1/2 mile south, then 3/4 mile east, and finally 1/2 milesouth. How many miles is he, in a direct line, from his startingpoint?

A digital watch displays hours and minutes with **am** and **pm**. What is the largest possible sum of the digits in the display?

Interactive version of problem and solution.

Interactive version of problem and solution.

Buy *Hexaflexagons, Probability, Paradoxes, and the Tower of Hanoi* from the MAA Bookstore

Let *S* be the set of all points with coordinates *(x, y, z),* where *x, y, *and *z *are each chosen from the set {0, 1, 2}. How many equilateral triangles have all their vertices in *S* ?

Interactive version of problem and solution.

Interactive version of problem and solution.

Three tiles are marked X and two other tiles are marked O. The five tiles are randomly arranged in a row. What is the probability that the arrangement reads XOXOX?

Kaleana, Quay, Marty and Shana discuss their test scores. Kaleana is the only one who shows her score to the others. Quay says, "At least two of us have the same score." Marty says, "I didn't get the lowest score." Shana adds, "I didn't get the highest score." Rank the scores from lowest to highest for Marty (M), Quay (Q) and Shana (S).

Interactive version of problem and solution.

Interactive version of problem and solution.

Gage skated 1 hr 15 min each day for 5 days and 1 hr 30 min each day for 3 days. How long would he have to skate the ninth day in order to average 85 minutes of skating each day for the entire time?

Interactive version of problem and solution.

Interactive version of problem and solution.

A traffic light runs repeatedly through the following cycle: green for 30 seconds, then yellow for 3 seconds, and then red for 30 seconds. Leah picks a random three-second time interval to watch the light. What is the probability that the color changes while she is watching?

Interactive version of problem and solution.

Interactive version of problem and solution.

For how many positive integers *n* does 1 + 2 + . . . + *n* evenly divide 6*n*?

Interactive version of problem and solution.

Interactive version of problem and solution.

Buy *Hexaflexagons, Probability, Paradoxes, and the Tower of Hanoi* from the MAA Bookstore

Sally has five red cards numbered 1 through 5 and four blue cards numbered 3 through 6. She stacks the cards so that the colors alternate and so that the number on each red card divides evenly into the number on each neighboring blue card. What is the sum of the numbers on the middle three cards?

Interactive version of problem and solution.

Interactive version of problem and solution.

A five-legged Martian has a drawer full of socks, each of which is red, white or blue, and there are at least five socks of each color. The Martian pulls out one sock at a time without looking. How many socks must the Martian remove from the drawer to be certain there will be 5 socks of the same color?

For a particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6 on each die are in the ratio 1 : 2 : 3 : 4 : 5 : 6. What is the probability of rolling a total of 7 on the two dice?

Interactive version of problem and solution.

Interactive version of problem and solution.

How many even three-digit integers have the property that their digits, read left to right, are in strictly increasing order?

Interactive version of problem and solution.

Interactive version of problem and solution.

Four distinct circles are drawn in a plane. What is the maximum number of points where at least two of the circles intersect?

Interactive version of problem and solution.

Interactive version of problem and solution.

Which of the following describes the graph of the equation (x + y)^{2} = x^{2} + y^{2} ?

The numbers -2, 4, 6, 9 and 12 are rearranged according to these rules:

1. The largest isn't first, but it is in one of the first three places.

2. The smallest isn't last, but it is in one of the last three places.

3. The median isn't first or last.

What is the average of the first and last numbers?

Interactive version of problem and solution.

1. The largest isn't first, but it is in one of the first three places.

2. The smallest isn't last, but it is in one of the last three places.

3. The median isn't first or last.

What is the average of the first and last numbers?

Interactive version of problem and solution.

Buy *Hexaflexagons, Probability, Paradoxes, and the Tower of Hanoi* from the MAA Bookstore

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