The Chocolate Problem

 

Drafter's Puzzle #2

A solid figure cut out of a cube looks like this in 2 dimensions when viewed from the front, back, and top.  Notice that it has a horizontal edge visible from the front but not from the top.  What could the solid look like?

Notice that it cannot look like this.  Otherwise we would see an edge from the top too!

What does the solid look like?  There are various possibilities. Click HERE for the solution.

Spatial thinking challenge

The figures below are all cut out of identical cubes.

The diagram below shows the front view of the figures in two dimensions.

Question:  What would the figures look like from the top in two dimensions?  Strangely, four of them look the same from above.  Which one is different?

For the solution, click HERE.

The Funny Calculator

A calculator has these buttons:

Just like a “normal” calculator,  

When you type 1 x 10, it says 10.

When you type 1 + 10, it says 11.

But…

When you type 1 + 1, it says 10.

When you type 10 + 10, it says 100.

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Using this information alone:

How would you count from one to four?  

What would the calculator say if you typed in 100 / 10 ?
    

Extending the pattern:


 Can you extend the pattern to count up to twenty?

What would the calculator say if you typed in 0.1 + 0.1?

What would the calculator say if you typed in 0.1 x 10 ?

What would the calculator say if you typed in 111 + 111 ?

What would the calculator say if you typed in 111 x 10 ?

For the solution, click HERE.

Counting triangles!

How many triangles are there in this picture?

It's not so easy.....

Did you say 7?  If so, you're right!

Watch this interactive video to practice organizing your thoughts when you solve counting problems:

Digital Clock Problem

The clock below uses columns of dots to represent the time, in minutes and hours.  What time does the clock read?

Use the clues below to decode the number system and read the time on the clock above.

Clues:

Here is the solution:

Each column represents a different power of 4.  And the number of dots tells you how many 1s, 4s, and 16s you have.  One way to see this is to start with the 8:04 clock and focus on the minutes.  It takes only one dot to make the number :04, so the single dot must have that value.  Then look at the 9:20 clock and again focus on the minutes.  It takes 2 dots to make :20.  One of those dots, we now know, is worth 4, so the other must be worth 16.  

All together the dots on the mystery clock represent:

4 + 4 + 1 + 1 hours, and

16 + 1 + 1 + 1 minutes, so

10:19

The Stacked Block Problem

Solution:  There are different ways to organize your thinking -- by row or by column.  There are 4 rows with a sum of 1 + 3 + 6 + 10 = 20.  Or 10 columns with a sum of 1 + 1 + 1 + 1 + 2 + 2 + 2 + 3 +  3 + 4 = 20.