# Help me improve the jumping robot problem

I recently posed a puzzle about Robot High and Robot Long

That puzzle was inspired by a comic I saw in Benjamin Bear in Fuzzy Thinking by Philippe Coudray. The particular comic is shown below:

As you can see in the edit history of the linked question, my original translation of the comic to puzzle added a bunch of numbers. This caused too much misdirection and calculations, though, and led many away from the intended solution. Based on comments and answers, I tried to generalize the problem. There were still a variety of responses, though, and many were valid.

I understand that the Puzzling community are clever and the tag really encourages open-ended thinking and comes with its own problems.

My question, therefore, is two-fold:

1. What's a better way to convert the comic to a puzzle intended for the Puzzling.SE community without resorting to a long list of caveats?
2. What down remove from that version and still have something that would still work for most "normal" people?
• I think I am failing to solve what that solution does at all. Note that this only works because the bear is much more massive than the bunny and (as a result) almost all of the posted questions would have worked...and the bunny jumping at all in probably unnecessary. – kaine May 11 '15 at 19:02

I don't think the puzzle in its original form would work here on PSE. There are too many loop holes to be closed before it has a single answer. It might work for 'normal' people but I still think you would need a fairly strong list of disallowed tactics. One of the main problems I think with your original two robots formulation, was that you made then the same size, and therefore presumably about the same mass. This makes the idea of one successfully bouncing off the top of the other seem a bit far fetched.

Closing the loop holes surrounding riding, carrying, stacking and shunting require you to be very specific about how the two bodies can interact in away that almost requires you to state, "The only way they can interact is for one to jump on the back of the other mid-jump." Obviously this is unsatisfactory as it effectively requires you to reveal the answer.

Here is how I would change it to work both here and anywhere else:

Rabbit is crossing a river hopping from one stone to another. A sudden surge of water washes away all but the stone rabbit is on. It is a little too far to either jump forward or jump back. Rabbit is trapped and would surely drown if she tried to swim across.

A wolf appears on the river bank licking its licks and says, "I'm going to jump over there and eat you little rabbit."

How does Rabbit escape?

The solution is about the only thing that remains unchanged. The change in setting removes the need for a long list of things that can't be done. By making the two bodies combatant rather than cooperative you avoid problems around riding and carrying, and it no longer matters if the wolf dies in the process.

The puzzle is somewhat easier as it is is now clear that the two bodies are travelling in opposite directions but that is the price to be paid for making the puzzle less open ended.

• This has taught me a valuable lesson: If I find puzzle inspiration somewhere, I shall boil it down to the clever element and then construct a puzzle that uses that element rather than trying to translate the entire situation. – Engineer Toast May 13 '15 at 13:52

This is the only way I can seem to make this make sense:

Pikachu and Donkey Kong are at one side of a narrow broken arch bridge. Donkey Kong can make the jump easy but needs his arms to get enough thrust. Pikachu can almost make the jump but not quite. The bridge is far too narrow and rickity for them to jump at the same time. Pikachu has a cold so can't hold on to Donkey without risking zapping him. How they they jump across?

Note: "up+B" is not the answer

• Alternate question: Nes is at a cliff and can't possibly jump the distance! But maybe he has a trick under his hat! Note: "up+B with 400%" is the answer :p – Mark N May 11 '15 at 19:27
• +1 for a reasonable explanation of why Pikachu can't ride or be carried – Rob Watts May 11 '15 at 20:23

If both sides of the gorge are at the same elevation, and if the rabbit and bear collide in the middle, the rabbit's effect on the bear's momentum will be worse than if the rabbit had simply been riding on the bear the whole time. The cartoon thus shows a cute, but unnecessarily complicated, way of solving the puzzle which could have been solved by simply having the bear carry the rabbit across.

I would suggest that a better puzzle could be had if one side of the gorge is higher than the other (e.g. by six feet), and both animals start on the lower side. In that case, if one of the animals is barely able to jump unassisted from the low side to the high side, then if that animal jumps from the high side it will have considerable excess elevation, and there might be scenarios where it could be used as a springboard, though one would have to define suitable rules for how horizontal and vertical velocity interact in such cases (in particular, you need to make sure that the horizontal motion of the abler jumper doesn't counteract that of the entity needing assistance). One could have robots with wheels that could be free-wheeled, but have the fronts and backs of the robots be very delicate such that the only collision that wouldn't cause damage would be one landing squarely on the top of the other and avoiding any transfer of horizontal momentum.

The puzzle might be further extended by having more than two robots with differing weights and abilities, such that robot #1 can jump by itself, robot #2 can jump on robot #1 while it's traveling back, robot #3 would need the assistance of both #1 and #2, etc.

I know for me, the way you worded your conditions were what threw me off. Specifically rules 7, 8, and 10.

The way rule 7 is worded, it seems like there is no physical way for High to be on top of Low.

Follow that by not adding any data about the sizes of the robots, as well as the generic jump data, you make it seem like, if High were to jump from atop Low, Low would be forced down too low and fall in the ravine.

And then Rule 8 forbids combining jumping power at all. Again, it seems like this is what is being done by launching off the other.

All in all, you were missing key data that the image presents. The bear is larger than the rabbit. The rabbit's downward force on the bear doesn't force it into the ravine. If you look at the answers and discussions on your post, many of them specifically state that there needs to be a size difference between the bots in order to work.

You also never explicitly state how the robots move, but your image depicts them with what appears to be wheels on the base. This leads to assumptions about locomotion that are not present in the picture above.

For example, my answer assumed that they rolled on wheels and that their stopped speed wasn't braked so the wheel would be free to move.

A more simplified way of stating the question could be as follows, (however it may make the answer seem a bit more apparent):

You have two jumpers Alice and Bob. Every 1 jump Bob does, Alice must take 2 to get the same distance Bob is much bigger and has more muscle than Alice which helps him jump further, but his jumps are much lower. While Alice is light and fast, she is able to jump much higher than Bob, but clearly not as far. Both Bob and Alice are hopping along until they found a cliff. Bob easily jumps across it and turns around to see Alice stuck. Alice isn't able to make the distance in 1 jump. There is nothing around in the environment to help her out either.

How can Alice get across the cliff?

Note: Bob is too big for Alice to be able to hold onto while jumping (and has no fur/hair to hang on by)

As some of the pitfalls in the previous riddle:

i) I think that the pictures were misleading in that the robots where always the same size (when in the comic they weren't).

ii) The mention about numbers (initially) or variables may misdirect people to approach the problem using math

iii) Rule 9: "The distances described for their jump limits are the furthest they can jump under the best circumstances." can imply that any attempt of interactions while jumping (or in air) would result in failure to make the distance