Wednesday, December 24, 2008

December 24, 2008

A 3 x 3 x 3 cube is formed by gluing together 27 standard cubical dice. (On a standard die, the sum of the numbers on any pair of opposite faces is 7.) The smallest possible sum of all the numbers showing on the surface of the 3 x 3 x 3 cube is?



Tuesday, December 23, 2008

December 23, 2008

Tyler has entered a buffet line in which he chooses one kind of meat, two different vegetables and one dessert. If the order of food items is not important, how many different meals might he choose?

Meat: beef, chicken, pork
Vegetables: baked beans, corn, potatoes, tomatoes
Dessert: brownies, chocolate cake, chocolate pudding, ice cream


Interactive version of problem and solution.



Monday, December 22, 2008

December 22, 2008

Of the 36 students in Richelle's class, 12 prefer chocolate pie, 8 prefer apple, 6 prefer blueberry, and as many of the remaining students prefer cherry pie as lemon. For Richelle's pie graph showing this data, how many degrees should she use for cherry pie?


Buy The Contest Problem Book VII

Friday, December 19, 2008

December 19, 2008

Yan is somewhere between his home and the stadium. To get to the stadium he can walk directly to the stadium, or else he can walk home and then ride his bicycle to the stadium. He rides 7 times as fast as he walks, and both choices require the same amount of time. What is the ratio of Yan's distance from his home to his distance from the stadium?

Interactive version of problem and solution.


Thursday, December 18, 2008

December 18, 2008

A faulty car odometer proceeds from digit 3 to digit 5 , always skipping the digit 4, regardless of position. For example, after traveling one mile the odometer changed from 000039 to 000050. If the odometer now reads 002005, how many miles has the car actually traveled?



Interactive version of problem and solution.






Wednesday, December 17, 2008

Tuesday, December 16, 2008

December 16, 2008

There are 24 four-digit whole numbers that use each of the four digits 2, 4, 5 and 7 exactly once. Only one of these four-digit numbers is a multiple of another one. Which one is it?


Buy Martin Gardner's Mathematical Games

Monday, December 15, 2008

December 15, 2008

Joe had walked half way from home to school when he realized he was late. He ran the rest of the way to school. He ran 3 times as fast as he walked. Joe took 6 minutes to walk half way to school. How many minutes did it take Joe to get from home to school?

Interactive version of problem and solution.




Friday, December 12, 2008

December 12, 2008

The sum of 18 consecutive positive integers is a perfect square. The smallest possible value of this sum is what?


Buy The Contest Problem Book VIII

Thursday, December 11, 2008

December 11, 2008

Call a set of integers spacy if it contains no more than one out of any three consecutive integers. How many subsets of {1, 2, 3, . . . ,12}, including the empty set, are spacy?




Wednesday, December 10, 2008

December 10, 2008

Six distinct positive integers are randomly chosen between 1 and 2006, inclusive. What is the probability that some pair of these integers has a difference that is a multiple of 5?

Interactive version of problem and solution.



Tuesday, December 9, 2008

December 9, 2008

The equations 2x+7 = 3 and bx – 10 = -2 have the same solution. What is the value of b?

Friday, December 5, 2008

December 5, 2008

Call a number "prime-looking" if it is composite but not divisible by 2,3, or 5. The three smallest prime-looking numbers are 49, 77, and 91. There are 168 prime numbers less than 1000. How many prime-looking numbers are there less than 1000?


Thursday, December 4, 2008

December 4, 2008

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.



Buy The Contest Problem Book IX

Wednesday, December 3, 2008

December 3, 2008

A set of 25 square blocks is arranged into a 5 x 5 square. How many different combinations of 3 blocks can be selected from that set so that no two are in the same row or column?




Buy The Contest Problem Book VIII

Tuesday, December 2, 2008

December 2, 2008

Let a, b, and c be real numbers such that a – 7b + 8c = 4 and 8a + 4bc = 7. Then a2b2 + c2 is?

Interactive version of problem and solution.



Buy The Contest Problem Book VIII

Monday, December 1, 2008

December 1, 2008

Blake and Jenny each took four 100-point tests. Blake averaged 78 on the four tests. Jenny scored 10 points higher than Blake on the first test, 10 points lower than him on the second test, and 20 points higher on both the third and fourth tests. What is the difference between Jenny's average and Blake's average on these four tests?



Buy The Contest Problem Book VII