January Problems

MP6: Attend to Precision

1/2/13 Sums and Products

What three consecutive counting

numbers have a sum that is 20% the

product of the three numbers?

1/3/13 Maximizing Regions

What is the greatest number of

regions you can get if you draw four

straight lines through a circle?

1/4/13 What’s the Rule?

Complete the table by determining the value of each letter. What rule is used to relate the numbers in the y column with those in the x column?

1/7/13 Alphanumeric Puzzle

Find the digits that represent the

letters E, F, G, and H to satisfy the

following puzzle. Each letter

represents a different digit. E F G H

x 4H G F E

1/8/13 Rabbits and Cages

Two rabbits each weigh the same. Two cages each weigh the same. If the total weight of the two rabbits and the two cages is 24 pounds, and the weight of one cage is 8 pounds, what does one rabbit weigh?

1/9/13 Solve this! Replace each letter with a different counting number from 1 to 10, inclusive. Each counting number is to be used only once. Each number must be the difference of the two above it. For example, E = A – B or B – A.

A B C DE F G

H JK

1/14/13 Zero the Hero!

Use each of the digits 1, 2, 4, 8 once

and only once to make at least two

different expressions that are equal to

0. You may use the operations +, –, x,

and ÷, but may use them more than

once. Parentheses may not be used.

1/15/13 1000’s the Limit!

If you add the consecutive counting

numbers starting with 1, what number

will cause the sum to exceed 1000?

Justify your answer.

1 + 2 =

3

1 + 2 + 3 = 6

1 + 2 + 3 + 4 = 10

1/16/13 Odd Constraints

Find an integer between 100 and 200

such that each digit is odd and the

sum of the cubes of the digits is equal

to the original three-digit number.

13 = 1; 23 = 8; 33 = 27,...

1/17/13 Tick Tock Sum

By drawing two straight lines, you

can divide the face of a normal

clock into three regions such that

the sum of the numbers in each

region sum to the same whole

number. What would be the

common sum?

1/18/13 A Prime Line

Arrange the integers 1 to 15 in a line

such that the sum of each adjacent pair

is a prime number. For example, 4, 1, 2,

3 would work since 4 + 1 = 5; 1 + 2 = 3;

and 2 + 3 = 5.

1/21/13 How Many Oranges?

A basket of fruit contains only bananas, apples and oranges. The basket contains 2 bananas, 6 red apples and 8 green apples. If the total number of pieces of fruit is three times the number of apples in the basket, how many oranges are in the basket?

1/22/13 Whoosh!

There are six teams in a

basketball league. Each team

plays each other team only

once during the season. How

many total games will be

played in the league during

the season?

1/23/13 Weight your turn

A groups of 6 women and 12 men

weigh a total of 3090 pounds. If

the women in the group have an

average weight of 125 pounds,

what is the average weight of the

men in the group?

1/24/13 What’s my number?

I am a number who is greater than

40 and less than 90. I am proud to

be a prime number. My ones digit is

also a prime number and so is my

tens digit. If you subtract my ones

digit from my tens digit, the answer

is not 2. Who am I?

1/25/13 Buying Books

At a bookstore, books A and B

together cost $45 (excluding

taxes). Two copies of book A and

3 copies of book B cost a total of

$125. At this bookstore, how

much is one copy of book A?

1/28/13 Three Landscapers

Three sisters run a landscaping

business. They charge $260 for each

job. If the oldest sister earns 50% more

than the middle sister, and the youngest

sister earns 50% less than the oldest

sister, how much does each sister earn

per job?

1/29/13 Cubes Not Squares!

What is the smallest perfect cube

(integer of the form n3) that is

divisible by 16 but is not a perfect

square?

13 = 1; 23 = 8; 33 = 27...

12 = 1; 22 = 4; 32 = 9...

1/30/13 A ☼ B

If A ☼ B means A – 3B, find all

possible values of x such that

x ☼ (2 ☼ x) = 1

1/31/13 Inscribe It Again

In the figure at the right, the smaller square is inscribed in a circle, which is inscribed in a larger square that is 8 x 8 cm. Approximately what percent of the figure is shaded?

adapted from NCTM’s Math Teaching in the Middle School Menu Problems

Mar 2006 & Oct 2007