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Triangular Numbers

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pinkee | 22:31 Sun 23rd Oct 2022 | Quizzes & Puzzles
14 Answers
Can someone help me with the following please:

Rearrange the numbers 1 to 21 so that the addition of adjacent triplets are a triangle number.
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Question Author
Not sure whether I've posted this.
Someone answere this the other day for someone
sorry that was you but that were Fibinachi numbers
I'd start same way as last time.
The numbers 1 to 21 add up to 231. Divide by 7 thats 33 I think. So each triplet must add up to 33
Then list the triangle numbers 1,3, 6, 10, 15, 21, 28 etc and arrange in blocks of 33
. I'm not sure thats going to work now though.
oh yeah I see - I did ask how the Fibonacci solver how they did it

traingular numbers - - 1 is a dot 3 is a dot with 2 dots under neath
6 is one dot - - - next row 2 dots and last row 3 dots

so I 3 6 are triangular numbers

I am not sure what an adjacent triplet is - - 11,12,13 perhaps, and the sum has to be a triangular number

and do the triplets overlap?
good start Bo-bo
yeah but no but - each have the same total
maybe I misundastood as I cant find any way's a getting 3 of them numbers to add up to 33... unless I need 2 pairs of triplets that add up to 66 but am too tired
Ignore mine.... its the numbers from the list 1 to 21 that have to be grouped and added to give traingular numbers.... I was wrongly adding triangular numbers. My bad


If it helps anyone google says the first triangular numbers are
^0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120,136, 153, 171, 190, 210, 231,

So its going to be alot easier than I made it
Question Author
I think you use the numbers 1 to 21 so if you used 2,3 and 5 that would up up to 10 which is a triangular number but you wouldnt be able to use those three individual numbers again. But you could use a different three which would make a different triangular number. You have to use all 21 nubers i think and come up with 7 griups of three
I assumed that any 3 adjacent had to add up to 21, so 19 groups not 7.
Its not the triplets tha as to be a triangle number, its the sum of two triples
so find 6 numbers from the list1-21 that add up to 66 which is trianguler. Say 1,2, 6 and 20, 19, 18
Then look for others and swap and change as needed.
Enjoy, am off to bed
easy way 1 +2 +3 + 21+20+19 = 66
4+5+6 +18+17+16 = 66
and so on
(1 +2 +3) + (21+20+19) = 66
(4+5+6) +(18+17+16 )= 66
7., 8,9 + 15,14,13 =66?
but that leaves 10 11 12

I really do give up. PP will solve it

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Triangular Numbers

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