A direct comparison in stride length in
Figure 1, along with simple geometrical relationships, will provide an
immediate solution to the puzzle: The wearer of high-heel shoes
experiences the shortening of each stride by...
That, presumably, makes the chase unfair, the catch easy. If you are curious about the three remaining choices, you will find that they are all correct -- or can be correct, depending on a few assumptions (see Vetruvian Man).
alking with only two feet is a precarious activity, if you stop to think about it, which few of us ever do. Walking is really what might be called "arrested falling." Notice that Figure 1 postulated the location of the walker's center of gravity (CG), generally at about the level of the navel. The CG serves a vital function in upright locomotion, for we observe that the CG must always be positioned some distance ahead of the back-most location of the walker's foot. The incipient fall is arrested by the action of the other foot, of course, when it strikes the surface in its forward-most position.
Perhaps you noticed in Figure 1 above that for the low-heel walker, the CG was assumed to be located directly above the hips. For the walker in high-heels, the hips will be drawn farther aft, closer to the back-most location of the walker's foot. That shortens the "moment arm" (leverage) for empowering forward motion, resulting in a slower walking speed. The remedy is elementary. The wearer of high-heeled shoes merely leans forward at the hip to move the CG to about the same horizontal location as that enjoyed by the wearer of low-heeled shoes. And the chase goes on.
igure 2 addresses another aspect of the walking challenge, keeping the body moving along at a constant elevation above the surface. The foot wearing a high-heeled shoe passing under the body during the stride will make lifting of the CG decidedly more pronounced. Pelvic roll can be applied to reduce the amount of vertical motion by lowering the hip connected to the forward-most leg. That does increase the flexing at the knee, however, which diverts some amount of the walker's effort, making the chase even more unfair.
All aesthetic considerations have been set aside in this analysis. The Chase Me, Catch Me puzzle is interested only in relative stride-length, to which we now return...
Shown in Figure 3 is the high-heel walker now deploying plenty of pelvic yaw, with the apparent intention of lengthening the stride -- recovering some of the disadvantage in the chase. The note in Figure 3 is salient, however, for we are reminded that the walker postulated for the low-heel reference stride does not make use of pelvic stratagems. Indeed, all proposed improvements in the high-heel stride must be offset by the fact that for this simplified (ceteris parabus) comparison, the low-heeled walker is unfairly constrained.
Ah, but there is not a dress-code on the planet that forbids the wearer of low-heeled shoes to go pitching, rolling, and yawing along the sidewalk enroute to workplace (backpacking a pair of high-heeled shoes, presumably).
Taking a range of heights for most likely wearers of high-heel shoes as 5' 4" to 5' 9", a median heel-height of 4", and a median low-heeled stride-length of 2' 6", we see the equivalance of....