## Sunday, September 1, 2019

### 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

## Friday, August 30, 2019

### 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.

## Thursday, April 11, 2019

### Domino Square Puzzle

There are 28 different dominoes in a set.  In the puzzle below, four dominoes from a set are placed in the shape of a square.  This is a "domino square."

We can make a puzzle out of a domino square by trying to arrange it so that we have the same number of "pips" (or dots) along each edge of the square.  It could be any number, it just has to be the same one each side.

Notice that the domino square below almost works -- it has 10 pips along three of the four edges, but the botton edge has only 7 pips.

Can you fix this square by replacing one of the dominoes so that every side has 10 pips?  Remember that the dominoes must all be different.

How many domino squares can you make with a single set of dominoes?