Triangular Numbers

[pinkee]

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.

[pinkee]

Not sure whether I've posted this.

[bobbinwales]

Someone answere this the other day for someone

[bobbinwales]

sorry that was you but that were Fibinachi numbers

[bobbinwales]

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.

[Peter Pedant]

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?

[Peter Pedant]

good start Bo-bo
yeah but no but - each have the same total

[bobbinwales]

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

[bobbinwales]

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

[bobbinwales]

^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

[pinkee]

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

[archibaldy]

I assumed that any 3 adjacent had to add up to 21, so 19 groups not 7.

[bobbinwales]

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

[bobbinwales]

easy way 1 +2 +3 + 21+20+19 = 66
4+5+6 +18+17+16 = 66
and so on

[bobbinwales]

(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