Yes folks, this is my 1100th post on aspiblog. I will start with a section on the number 1100, provide a number of autism related links and include some of my own photographs.
1,100 = 2 * 2 * 5 * 5 *11.
An ammunition store that contained 20 complete pyramids of cannon-balls each with a base side length of 5 cannonballs would contain a total of 1100 cannonballs:
(1 + 4 +9 + 16 +25) = 55, 55 * 20 = 1,100.
These same cannon balls could also have been stacked in five tetrahedrons each with a base side length of 10.
(1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55)= 220, 220 * 5 = 1,100
However, it was standard to stack cannon balls in pyramids, and also a the single cannon ball on top of a stack 10 cannonballs high might be rather difficult to reach.
Another option on the pyramidal theme would be a single truncated pyramid with base side length 15 cannonballs, and the top layer of the pyramid having a side length of 64 (225 + 196 + 169 + 144 + 121 + 100 + 81 + 64 = 1,100.
As a teaser what is the minimum base size length needed to stack 1,100 cannonballs in a single truncated tetrahedron, and what if you restrict yourself by insisting that each layer must be a perfect triangle?
AUTISM RELATED LINKS
This section is devoted to autism related stuff, so the text, including links which will be in bold and underlined, is all in #RedInstead. My first link comes from the blog aliensfromplanetautism under the title “What Autism Acceptance Means” Below is a screenshot of the start of the post:
My next offering is also courtesy of thesilentwaveblog, under the title ‘Taking the “pity” out of serendipity‘. It also features an excellent picture, reproduced below.
While my next choice is not specifically about autism it is produced by an autistic blogger, unabashedautist. Published under the title “Signals, Jerry. Signals.“, it features a graphic which I just had to share with you as I do below, not least because it has been declared illegal in Russia.
Now we turn back to thesilentwaveblog and a piece with the title “Asperger’s / autism and self-acceptance (#IveLearnedToAccept)“. This post also features a splendid picture, reproduced below.
My next link, and the last before I move into a new subsection (still autism related), comes courtesy of BadassAmericanAdvocates guest writer Anonymously Autistic Anna. Titled “PLEASE READ AUTISTIC PERSPECTIVES THIS AUTISM AWARENESS / ACCEPTANCE MONTH“, it is truly a must read. I have included a screenshot of the opening paragraphs below.
THE AUTISM AWARENESS CUP
Bookings are now open for the second running of the Autism Awareness Cup six-a-side football tournament, which takes place at Ingoldisthorpe Social Club on June 4th (and it is free btw). If you are able to come along please click on the graphic below to book:
ANSWERS TO TEASER
The second part of the teaser was a trick question – there is no combination of consecutive triangle numbers that adds up to 1,100, therefore a perfect truncated tetrahedron is not possible. The first part of the answer is that you can make a truncated tetrahedron of 1084 cannon balls from a base with side length 18 up to side length 7, but there are then only 16 balls left for the next layer which is therefore incomplete.