# Thread: Magic Triangle - Easy

1. ## Magic Triangle - Easy

Insert the digits 1...9 into each of the smaller triangles below so that:
1. Each of the three inner triangles (made up of 4-cells) add to 23, and
2. Each of the three inner trapezoids (made up of 5-cells) add to 22.

The two lower triangles below are there to demonstrate what an inner traingle and an inner trapezoid look like. The upper trinagle is all blank and where the digits 1...9 should be entered.

2. ## Re: Magic Triangle - Easy

Here is one solution.

3. ## Re: Magic Triangle - Easy

If you want to know how I found this:
<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>I wrote down all combinations of four numbers in the range 1 through 9 that add up to 23. There are 9 such combinations:</font color=yellow></span hi><pre><span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>A: 1 5 8 9
B: 1 6 7 9
C: 2 4 8 9
D: 2 5 7 9
E: 2 6 7 8
F: 3 4 7 9
G: 3 5 6 9
H: 3 5 7 8
I: 4 5 6 8</font color=yellow></span hi></pre>

<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>These numbers constitute the potential "inner triangles". We need three "inner triangles", of which each pair only has one number in common. I started with A. The only ones that only have one number in common with A are E and F. It's easy to draw the complete triangle from these - you can even swap some numbers without disturbing the solution (1 and 5, for instance). By finding other triples whose pairs have only one number in common, it is possible to construct other solutions, e.g. from B, C and H.</font color=yellow></span hi>

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•