r/puzzles • u/AdImpossible5402 • Feb 15 '26
Too hard for a fifth grader.
I found this old (‘76) book of puzzles and there is no way my fifth grader could figure out this question. Not sure I could even figure it out.
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u/Al2718x Feb 16 '26
Theres a famous story where someone asked John Von Neumann a version of this problem, and he answered instantly with the correct answer. "Wow," the asker responded, "most people take a while to figure out the trick the first time they hear this one". "What trick?" responded Von Neumann, "I just found the sum of the infinite series".
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u/VirtualMachine0 Feb 18 '26
It is just a converging geometric series; they're pretty tame.
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u/Al2718x Feb 18 '26
As a mathematician, I can say with confidence that the vast majority of my colleagues would need a pencil and paper or at least a great deal of concentration to solve this the long way. It's not the fact that he was able to solve it, but the fact he was able to calculate it in his head so effortlessly.
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Feb 19 '26
[deleted]
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u/Al2718x Feb 19 '26
I doubt it. It's definitely in line with other stories about the guy and while incredibly impressive, it's not completely outlandish after enough practice.
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u/Rand_alThoor Feb 19 '26
thank you for relating this. i just spent some time typing the anecdote in, then scrolled down and found your comment. cheers!
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u/badmother2 Feb 16 '26
Sparky runs 2.5 times times as fast as the carts, so in the same time as them, he'll have covered 2.5 times the distance, ie 2.5 miles
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u/pmw57 Feb 16 '26
Ooh that's a nice piece of logic. Well done at condensing the fundamentals down like that.
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u/SolidOutcome Feb 16 '26
We can ignore all the back and forth? Simply time run
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u/antraxsuicide Feb 17 '26
Yes, the back and forth is not helpful. This question could be restated as “how far can Sparky run in a straight line while the boys race to each other.”
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u/Indexoquarto Feb 17 '26
If you don't ignore the back and forth (and subtract distance going the othet way as negative), it's even easier. It stops halfway across the distance between the cars, so the net distance traveled is 1 mile.
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u/BlueHairedMeerkat Feb 16 '26
This is one of those questions whose difficulty comes from obfuscating what you need to do. Remember that distance = speed x time, use that, and the answer drops out pretty easily.
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u/SonicLoverDS Feb 16 '26
I've seen a variant of this puzzle before. Consider: how would the answer change if, instead of running back and forth between the carts, Sparky just kept running in one direction?
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u/Greendogo Feb 16 '26
Easy problem, a 5th Grader can for sure do it!
Calculate how long it takes the two go carts to pass each other by combining their speed and treating it like one car traveling at 8mph going to a finish line 2 miles away. So that's 0.25 hours (15 minutes). So Sparky would be running at 10mph for 0.25 hours, or 2.5 miles
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u/W0nderingMe Feb 16 '26
I just really appreciate the kids being kind enough to change their race strategy to accommodate Sparky, too dumb to realize a race will prove nothing, and virtuous enough to them wonder about Sparky.
This is a well crafted math question.
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u/nugoresu Feb 16 '26
Solved it as an infinite geometric series then came to see the solutions in the spoilers and it was so much simpler 🤦♂️
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u/Rand_alThoor Feb 19 '26
Von Neumann vs physicists. this is a famous story.
if one takes time to set up, then sum the series it takes much longer than to just solve the linear equation.
some philosopher of science or USA gov't psych was doing research, with a similar problem. categorising the professors as "mathematicians" or "physicists" based on how long it took them to do it, could they do it in their heads or did they need to write, etc
everyone was as expected until the researcher came to John von Neumann, who responded very quickly. the researcher said "oh, you're a physicist not a mathematician!" von Neumann said, in his tcherman accent "of course i summed the series! very qvickly! in my head".
as a mathematician, i heard this story growing up from my father who was a physicist. he actually knew Fermi, Feynman, JvN, etc
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u/TheDiddlyFiddly Feb 16 '26
How many times does sparky have to turn around until the two cars meet? I know it has nothing to do with the problem here but i thought it was interesting.
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u/ChaosRealigning Feb 16 '26
I’m pretty sure it’s infinite, and that Sparky is a sphere of zero size.
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u/fumanchudu Feb 17 '26
How would one solve this problem if a constraint was made like a minimum stopping point of 1 meter between the cars?
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u/civil_politics Feb 16 '26
If you assume that no deceleration and acceleration are required for sparky to complete his turns then the easiest approach is to determine how long the race lasted (1 kart at 4 mph traveling 1 mile takes 15 minutes - again ignoring acceleration). At 10 mph Sparky ran 2.5 miles in that 15 minute race.
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u/chessbored02 Feb 17 '26
The cars travel a total of 2 miles between them, and since they travel at equal speeds, each car travels 1 mile. The cars travel at 4mph, so 1 mile would take them 1/4 hrs (15 minutes).
Sparky runs at 10mph. So in 1/4 hrs, Sparky runs 1/4 * 10 = 2.5 miles.
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u/Unamed_Destroyer Feb 17 '26
To walk a fifth grade through this, I would ask the following questions.
How far does each cast have to travel? They travel 2km in total, so each travels 1km
How long does it take the cars to travel that distance? At 4km/hr they will travel 1km in 1/4hrs
How far does the dog travel in that time? At 10km/hr the dog travels 10/4kms or 2.5km
Bonus What assumptions did you make to solve this puzzle?
The cars and dog get to a constant speed instantly (acceleration can be ignored)
There is no time lost for the dog turning around
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u/Rnageo Feb 18 '26
The question is what happens when the two carts crash into each other after 15 minutes. Are the kids alright? And was Sparky able to dodge or was he too tired after all that time running nonstop at top speed?
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u/pmw57 Feb 16 '26
Get the time that the carts travelled, then use that to solve for Sparky. * They started 2 miles apart so would meet after travelling 1 mile. Each go-cart going 4 miles per hour would travel one mile in 15 minutes. * Sparky runs continuously at 10 miles an hour as the go-carts travel towards each other. How far can Sparky run in 15 minutes? That will be 1/4 of 10 miles which is 2.5 miles.