Answer:

The precise amount of reps and sets for optimal results is not known, and everyone responds differently. Abdominal muscles are no different than any other skeletal muscles and so theoretically they should respond to the same stimulus, but of course, most people do more than just 3 sets of 10-12 reps, and many people work them multiple times per week. The abs do move your body in multiple directions or planes, and there are lots of fibers, so there is some justification for all the different ab exercises to stimulate all those fibers, and justification for doing multiple sets and/or reps.

In addition, the abs are "anti-gravity" muscles, which means they support your posture and work most of the time, which means that one approach is to train them with high reps and more frequently than other muscle groups. A good approach is to do some of the sets for strength (about 10 reps), and then sets for endurance (15-20 reps), and a variety of exercises. Every other day as you are doing sounds right. Whatever number or exercises you do, make sure you do them slowly and with good form, and that you are fatigued at the end of each set.

Another factor in your results is the amount of excess fat you have on your abdomen. The "six-pack" that you see on some individuals has a lot to do with how lean the abdomen is (and toned muscles, of course). The leaner they, are the more likely you will be to see the muscles. Reducing your abdominal body fat is desirable if you want results that you can see. If you are looking to tighten up and even decrease your girth, that will happen sooner than the six-pack appears since the abs will tighten rather quickly in response to most training, and you may even notice that your slacks fit looser before you see any tone.

Here's some information about abdominal exercises that you may find helpful.

A recent study at San Diego State University measured the electrical activity of the abdominal muscles during different abdominal exercises to determine which exercises generated the most muscle activity. The researchers used electromyography (EMG), a sophisticated machine that measures muscle activity. They measured the rectus abdominis (the front of your abs, from the upper to the lower abs), as well as the obliques (the sides). As for differentiating the upper and lowers, it was found that the subjects could not trigger a contraction in one particular part of the abs, but rather that the upper and lower abdominals act as a sheath.

Here are the results and descriptions of the top five exercises. The captain's chair is done on a knee-raise stand (the type where you can rest your elbows), and the Hover exercise was not described. Please note that EMG values are listed as a percentage of the activity generated by a traditional crunch. For instance, a long arm crunch yields 19% more activity for the rectus abdominis than the crunch; and a vertical leg crunch yields 116% more activity for the obliques than the crunch.

Activity in Rectus Abdominis
Rank -- Exercise -- Mean % of activity

1. Bicycle maneuver 248
2. Captain's chair 212
3. Exercise ball 139
4. Vertical leg crunch 129
5. Torso track (machine) 127
6. Long arm crunch 119
7. Reverse crunch 109
8. Crunch with heel push 107
9. Ab roller (machine) 105
10. Hover 100
11. Traditional crunch 100
12. Exercise tubing pull 92

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Activity in Obliques
Rank -- Exercise -- Mean % of activity

1. Captain's chair 310
2. Bicycle maneuver 290
3. Reverse crunch 240
4. Hover 230
5. Vertical leg crunch 216
6. Exercise ball 147
7. Torso track (machine) 145
8. Crunch with heel push 126
9. Long arm crunch 118
10. Ab roller (machine) 101
11. Traditional crunch 100
12. Exercise tubing pull 77

1.Bicycle Maneuver: Lie flat on the floor with your lower back pressed to the ground. Put your hands beside your head. Bring knees up to about 45-degree angle and slowly go through a bicycle pedal motion. Touch your left elbow to your right knee, then your right elbow to your left knee. Keep even, relaxed breathing throughout.

2. Captain's Chair: Stabilize your upper body by gripping the hand holds and lightly pressing your lower back against the back pad. The starting position begins with you holding your body up with legs dangling below. Now slowly lift your knees in toward your chest. The motion should be controlled and deliberate as you bring the knees up and return them back to the starting position.

3. Crunch on Exercise Ball: Sit on the ball with your feet flat on the floor. Let the ball roll back slowly. Now lie back on the ball until your thighs and torso are parallel with the floor. Cross your arms over your chest and slightly tuck your chin in toward your chest. Contract your abdominals, raising your torso to no more than 45 degrees. For better balance, spread your feet wider apart. To challenge the obliques, make the exercise less stable by moving your feet closer together. Exhale as you contract; inhale as you return to the starting position.

4. Vertical Leg Crunch: Lie flat on the floor with your lower back pressed to the ground. Put your hands behind your head for support. Extend your legs straight up in the air, crossed at the ankles with a slight bend in the knee. Contract your abdominal muscles by lifting your torso toward your knees. Make sure to keep your chin off your chest with each contraction. Exhale as you contract upward; inhale as you return to the starting position.

5. Reverse Crunch: Lie flat on the floor with your lower back pressed to the ground. Put your hands beside your head or extend them out flat to your sides --whatever feels most comfortable. Crossing your feet at the ankles, lift your feet off the ground to the point where your knees create a 90-degree angle. Once in this position, press your lower back on the floor as you contract your abdominal muscles. Your hips will slightly rotate and your legs will reach toward the ceiling with each contraction. Exhale as you contract; inhale as you return to the starting position.

Because the hip flexor muscles work during ab exercises (which might take a way from the work of the abs), the researchers measured that, too, and found that the exercise ball, even though it did not generate the most activity in the rectus abdominis and obliques, did generate significantly less activity in the hip flexor. They reported that because of this, the exercise ball may be the best overall ab exercise of the exercises studied.