Question 1

If posts are spaced 11 feet apart, how many posts are needed for 99 feet of straight-line fence?
​
__________ posts
​

Accepted Answer

The answer of If posts are spaced 11 feet apart,...

Question 2

If posts are spaced 14 feet apart, how many posts are needed for 98 feet of straight-line fence? ​

Accepted Answer

Since the posts are spaced 14 feet apart, divide 98 feet by 14 to get the number of posts needed: 98/14 = 7. The fence needs 7 posts, so the best choice is B.

Question 3

If a family has 4 children, in how many ways could the parents have 2 boys and 2 girls as children?
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__________ ways
​

Accepted Answer

The answer of If a family has 4 children, in...

Question 4

There are four separate, equal-size boxes, and inside each box there are two separate small boxes, and inside each of the small boxes there are three even smaller boxes. How many boxes are there all together?
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__________ boxes
​

Accepted Answer

The answer of There are four separate, equal-size boxes, and...

Question 5

If an island's only residents are penguins and bears, and if there are 17 heads and 38 feet on the island, how many penguins and how many bears are on the island?
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The number of bears is __________.
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The number of penguins is __________.
​

Accepted Answer

The answer of If an island's only residents are penguins...

Question 6

Ten full crates of walnuts weigh 390 pounds, whereas an empty crate weighs 5 pounds. How much do the walnuts alone weigh?
​
__________ pounds
​

Accepted Answer

The answer of Ten full crates of walnuts weigh 390...

Question 7

Alex, Beverly, and Cal live on the same straight road. Alex lives 9 miles from Beverly and Cal lives 4 miles from Beverly. How far does Alex live from Cal?
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If there is more than one answer, separate them with commas.
​

Accepted Answer

The answer of Alex, Beverly, and Cal live on the...

Question 8

Thoth, an ancient Egyptian god of wisdom and learning, has abducted Ahmes, a famous Egyptian scribe, in order to assess his intellectual prowess. Thoth places Ahmes before a large funnel set in the ground (see figure below). It has a circular opening 1,000 ft in diameter, and its walls are quite slippery. If Ahmes attempts to enter the funnel, he will slip down the wall. At the bottom of the funnel is a sleep-inducing liquid that will instantly put Ahmes to sleep for eight hours if he touches it. Thoth hands Ahmes two objects: a rope 1,006.28 ft in length and the skull of a chicken. Thoth says to Ahmes, "If you are able to get to the central tower and touch it, we will live in harmony for the next millennium. If not, I will detain you for further testing. Please note that with each passing hour, I will decrease the rope's length by a foot. How can Ahmes reach the central ankh tower and touch it?
​  ​
Ahmes' dilemma. Note that there are two ankh-shaped towers. One stands on a cylindrical platform in the center of the funnel. The platform's surface is at ground level. The distance from the platform surface to the liquid is 500 ft. The other ankh tower is on land, at the edge of the funnel.
​

Accepted Answer

The answer of Thoth, an ancient Egyptian god of wisdom...

Question 9

How many 1-cent stamps are there in a dozen?
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__________ stamps
​

Accepted Answer

The answer of How many 1-cent stamps are there in...

Question 10

If you take 5 cards from a deck of 65 cards, how many cards do you have? ​

Accepted Answer

If you take 5 cards from a deck of 65 cards, you will have 5 cards.

Question 11

If you take 7 cards from a deck of 52 cards, how many cards do you have?
​
__________ cards
​

Accepted Answer

The answer of If you take 7 cards from a...

Question 12

Thoth, an ancient Egyptian god of wisdom and learning, has abducted Ahmes, a famous Egyptian scribe, in order to assess his intellectual prowess. Thoth places Ahmes before a large funnel set in the ground (see figure below). It has a circular opening 1,000 ft in diameter, and its walls are quite slippery. If Ahmes attempts to enter the funnel, he will slip down the wall. At the bottom of the funnel is a sleep-inducing liquid that will instantly put Ahmes to sleep for eight hours if he touches it. Thoth hands Ahmes two objects: a rope 1,006.28 ft in length and the skull of a chicken. Thoth says to Ahmes, "If you are able to get to the central tower and touch it, we will live in harmony for the next millennium. If not, I will detain you for further testing. Please note that with each passing hour, I will decrease the rope's length by a foot. Is it possible to reach the central ankh tower and touch it? ​  ​
Ahmes' dilemma. Note that there are two ankhshaped towers. One stands on a cylindrical platform in the center of the funnel. The platform's surface is at ground level. The distance from the platform surface to the liquid is 500 ft. The other ankh tower is on land, at the edge of the funnel.
​

Accepted Answer

The answer of Thoth, an ancient Egyptian god of wisdom...

Question 13

There are 5 separate, equal-size boxes, and inside each box there are 4 separate small boxes, and inside each of the small boxes there are 3 even smaller boxes. How many boxes are there all together? ​

Accepted Answer

There are 5 large boxes, each containing 4 small boxes, and each small box contains 3 even smaller boxes. So, the total number of boxes is 5 + (5*4) + (5*4*3) = 5 + 20 + 60 = 85 boxes.

Quiz 1: The Nature of Problem Solving

If posts are spaced 11 feet apart, how many posts are needed for 99 feet of straight-line fence? __________ posts

If posts are spaced 14 feet apart, how many posts are needed for 98 feet of straight-line fence?

If a family has 4 children, in how many ways could the parents have 2 boys and 2 girls as children? __________ ways

There are four separate, equal-size boxes, and inside each box there are two separate small boxes, and inside each of the small boxes there are three even smaller boxes. How many boxes are there all together? __________ boxes

If an island's only residents are penguins and bears, and if there are 17 heads and 38 feet on the island, how many penguins and how many bears are on the island? The number of bears is . The number of penguins is .

Ten full crates of walnuts weigh 390 pounds, whereas an empty crate weighs 5 pounds. How much do the walnuts alone weigh? __________ pounds

Alex, Beverly, and Cal live on the same straight road. Alex lives 9 miles from Beverly and Cal lives 4 miles from Beverly. How far does Alex live from Cal? If there is more than one answer, separate them with commas.

How many 1-cent stamps are there in a dozen? __________ stamps

If you take 5 cards from a deck of 65 cards, how many cards do you have?

If you take 7 cards from a deck of 52 cards, how many cards do you have? __________ cards

There are 5 separate, equal-size boxes, and inside each box there are 4 separate small boxes, and inside each of the small boxes there are 3 even smaller boxes. How many boxes are there all together?

Quiz 1: The Nature of Problem Solving

If posts are spaced 11 feet apart, how many posts are needed for 99 feet of straight-line fence? ​ __________ posts ​

If posts are spaced 14 feet apart, how many posts are needed for 98 feet of straight-line fence? ​

If a family has 4 children, in how many ways could the parents have 2 boys and 2 girls as children? ​ __________ ways ​

There are four separate, equal-size boxes, and inside each box there are two separate small boxes, and inside each of the small boxes there are three even smaller boxes. How many boxes are there all together? ​ __________ boxes ​

If an island's only residents are penguins and bears, and if there are 17 heads and 38 feet on the island, how many penguins and how many bears are on the island? ​ The number of bears is __________. ​ The number of penguins is __________. ​

Ten full crates of walnuts weigh 390 pounds, whereas an empty crate weighs 5 pounds. How much do the walnuts alone weigh? ​ __________ pounds ​

Alex, Beverly, and Cal live on the same straight road. Alex lives 9 miles from Beverly and Cal lives 4 miles from Beverly. How far does Alex live from Cal? ​ If there is more than one answer, separate them with commas. ​

How many 1-cent stamps are there in a dozen? ​ __________ stamps ​