How many different triangles can be formed from four rods with lengths of 1 meter, 3 meters, 5 meters, and 7 meters?

Since there is no angle restriction in this case, therefore the one rule that is applicable to this is that in forming a triangle, the sum of the lengths of the two smaller sides (A + B) should be larger than the length of the biggest side (C):

Triangle length rule: Side A + Side B > Side C

We can see that no matter how we combine the rods, the only combination of rods that satisfies this rule is:

Triangle formed by rods 3 meters, 5 meters, and 7 meters

Therefore, there is only 1 triangle that can be formed from these four rods.