Peegue's Puzzle Page
Welcome to Peegue's Puzzle Page. Logic Puzzles, Mazes, and more... Peegue is always on the look-out for interesting puzzles for you to ponder and solve. For this edition, Peegue has a very mathematical puzzle for you. Enjoy!
Peegue is looking at a large triangle, and decides to place an up-side
down triangle of half size inside it. The resulting shape now contains
five triangles: the original large triangle, and four triangles on the
inside (see "Step 1" below).
Peegue repeats this process, placing a smaller up-side triangle into
each of the right-side up triangles (see "Step 2" below). Counting all
triangles, Peegue finds one large triangle, four medium triangles, and
twelve small triangles, for a total of 17 triangles in his picture.
Peegue is considering repeating this process a number of times, but has
1. What if Peegue were to repeat this process all the way up to "Step
10"? How many triangles of any size would the resulting picture have?
2. How many triangles would a picture of "Step 20" contain?
3. If drawing each triangle takes Peegue just one second, how long would
it take Peegue to draw the "Step 20" picture?
Hint: start by counting the triangles in Step 3, then drawing Step 4 and
counting its triangles. Look for a pattern (it might help to not just
look at the total number of triangles, but subdivide the triangles into
sizes "large, medium, small, smaller, even smaller..."). To get the final
answer, you might want to keep a calculator handy.
This puzzle might take some time to work out, so don't give up too easily. Make time on a Sunday morning, grab a cup of tea or coffee, put your thinking cap on, and let possible solutions percolate in your mind.
If you think you have the answer (or you -gulp!- give up), you can send Peegue an e-mail at
email@example.com. You will receive an automated reply with the link to the solutions. (Make sure that you add Peegue to your address-book if you use a spamfilter, so that the reply doesn't land in your junk folder).
Peegue is also always interested in hearing about new puzzles from all around the world. If you've come across an interesting puzzle that you think Peegue would like to know about, just e-mail us.