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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 three questions.

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 peegue@midnightsynergy.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.

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