Can you name the missing Pythagorean triples?

created by ysumath

Enter an answer in the box below
Correctly named answers will show up below
Click any empty Pythagorean Triples or Missing Triple to answer for that location
All triples are less than 100 and in non-decreasing order.
Also try: Prime Numbers

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Pythagorean Triples	Missing Triple
3, 4, ?
5, 12, ?
8, 15, ?
7, 24, ?

Pythagorean Triples	Missing Triple
20, 21, ?
12, 35, ?
9, 40, ?
28, 45, ?

Pythagorean Triples	Missing Triple
11, 60, ?
33, 56, ?
16, 63, ?
48, 55, ?

Pythagorean Triples	Missing Triple
13, 84, ?
36, 77, ?
39, 80, ?
65, 72, ?

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There are 17 comments for this game.
(Warning: comments may contain spoilers)

Missing Pythagorean Triples Quiz

by ysumath

Created May 2, 2011 in Science
Featured Oct 13, 2012
Game Plays 4,023

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Archived comments: show them

	Headers2304:	Oct 13th, 2012 at 16:05 GMT		3 points
	Great quiz, and very tough! :)

	Kiratroid:	Oct 13th, 2012 at 17:22 GMT		2 points
	This trick works for some of the ones where the lowest of the triple is an odd number. Square it and divide by 2. Rounding up and down will get you the last two numbers. e.g. 15, 112, ? 15^2=225. 225/2=112.5 Rounding up and down gives 112 and 113. So your triple is 15, 112, 113.

	biziclop:	Oct 13th, 2012 at 17:30 GMT		1 point
	Another trick is that they're either all even (in which case they can all be divided by 4, so they're not "raw" triples) or two of them are odd and one of them is even. So given two of them, the parity of the third is already known. That's 50% less numbers to try :)

	biziclop:	Oct 13th, 2012 at 17:31 GMT		1 point
	"they can all be divided by 4" -> "their squares can all be divided by 4"

	Spencer_Hastings:	Oct 13th, 2012 at 17:35 GMT		5 points
	SPOILER: All the answers are congruent to 1 mod 4. Combine that with the fact that they go in ascending order ....

	Ulkomaalainen:	Oct 13th, 2012 at 21:36 GMT		3 points
	@buj/randomguess (from the archives): the correction of course is true. And funny enough you can prove that via comparing results from the first and second binomial theorems when you split a number into the last digit and the remainder (which will be divisible by 10). Oh, the joy of maths - haven't had this much fun in a loooong time - kidding ;)

	Degree:	Oct 13th, 2012 at 23:01 GMT		3 points
	This would be tougher if they weren't necessarily in non-decreasing order. Having known a few, with the time limit it's perfectly possible to cycle through the rest and get them all. Fantastic quiz otherwise though, amazing how many basic triples under 100 I didn't actually know off the top of my head.

	etes97:	Oct 14th, 2012 at 00:09 GMT		1 point
	This is awesome quiz!! It was harder than I expected, though....

	geome12:	Oct 14th, 2012 at 17:09 GMT		0 points
	too much time... finished with 2:49 by randomly guessing odd numbers. all of them are odd.

	Speenatch:	Oct 15th, 2012 at 04:17 GMT		5 points
	What worked for me was to look only at the last digit of the two numbers. 8 and 5? Well, we know the third number will end in a 9. Then just try every _3 and _7 in increasing order.

	defineexistence:	Oct 15th, 2012 at 19:29 GMT		1 point
	I would recommend placing the questions in a random order. As some of the others have posted, once you can get the ones you know, it's not too hard to guess numbers that are greater than the second number and in between other answers.