The King of Puzlandia has designed a new national flag for his country as shown above. He specifies that the flag should be 5 feet high and 7.5 feet wide, and that the two colors should have exactly the same area (he wants to use the same amount of light and dark blue cloth in each flag). How wide must the dark blue stripe be?
Extra credit: The flag makers of the kingdom aren't very good with complex math. Can you come up with a simple rule for determining the width of the stripe for any size flag (with this same ratio of height to width ratio, of course)?
The chessboard factory in Puzlandia has produced some “irregular” chessboards. Can you find a way to cut this chessboard into two pieces and reassemble it into a proper chessboard (with the white and black pattern intact)? It would be easy to cut off the two white squares and move them, but that would require cutting the board into three pieces.
The Flash video below shows the solution to the puzzle:
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SOLUTION:
This puzzle is credited to Henry Ernest Dudeney (1857-1930).
Find cubes of whole numbers whose digits add up to the value of their cube root.
For example: 512 is the cube of 8, and 5+1+2 = 8.
“1” is another (rather trivial) example. There are four others.
SOLUTION:
The only whole numbers whose cubes fit this criteria are 1, 8, 17, 18, 26, & 27. Here's a chart showing the cubes from 1 to 63.
It's interesting to note that once you reach 54, whose cube has 6 digits, it seems impossible for there to be larger numbers that meet the criteria, since the total of the digits of the largest possible 6 digit number (999999) is 54. The largest possible total from a 7 digit number would be 63, while the smallest number that has a 7-digit cube is, of course, 100.
Can anyone formulate a mathematical proof with 54 (or any lower number) as a limit? Send your input to editor@automationnotebook.com
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