At least he wasn’t doubling grains of sand on 64 chess squares!
1 Like
Fortunately not ! (nor was he dealing out a deck of 52 playing cards 
)
We had £20 worth of 2p pieces, so still well short of the number required to create Heap No. 58.
NB. We are only talking about Heap 58 itself. Not all the heaps 1 to 58 together.
For heap 58, there will be 58 rows ranging from 1 coin to 58 coins.
Which is equivalent to 58 rows with an average of 29.5 coins.
Which equates to 1711 coins.
I calculated it in my head - 58 x 30 less half of 58.
3 Likes
There is a pattern that achieves this though it took me a while to spot it. Once the method is known it can be done in one’s head for 58.
Anyone want to attempt it?
1 Like
Well, my reckoning suggests 34,220 coins are required to fill all 58 heaps.
As for specific mental arithmetic patterns … I struggled with 58 x 59/2 in my head, even though I did something similar to what SteveD did for the 1711 coins in the first part of the teaser.
1 Like
Agreed.
@SteveD explained the 1,711 perfectly. The general formulae look like this:
(n+0)/1 = n heaps
(n+0)/1 x (n+1)/2 coins in n heaps
(n+0)/1 x (n+1)/2 x (n+2)/3 coins in n heaps of heaps
etc
Hence the answer is 1,711 x 20 = 34,220
1 Like
Probably also for 28 … (it was a bit of a struggle)
I even found it OK with 14 … by careful “cancelling down” I found I could do 7x8x10=560 in my head.
…and 13 using 13x7x5=455
But I couldn’t do 60 in my head !! (it was the 61x62 part in which I failed)
Nonetheless, well done Ravvie. A very neat solution. And a nice development of Steve’s solution.
Well done Steve. I think your explanation of your mental arithmetic sparked a few more ideas in both myself and Ravvie concerning mental maths. Nice one
1 Like
Hi Don,
my solution for the simple sums looks like this:
My starting point was the second column. The third number had to be 4, because there is already a 6 in the third row. This leaving only the 6 as the fourth number in the column.
Nicely done Mulberry and a very nice explanation of how you got started - same route that I took.
I hope you enjoyed the teaser.
I’ve had a few ‘computer’ issues this past few weeks. (Real brain teasers !!)
Unreliable internet; John Lewis withdrawing its Broadband and e-mail accounts; Windows 11; Microsoft 365; PowerPoint no longer accepting direct scan imports; new printer requires the internet to download operating system and then monitor usage …… the list goes on ! But beginning to see a light at the end of a tunnel, so to speak !
I’ve put together a few more Brain Teasers and will post one or two of them later this evening – so as to give our Antipodean friends time to enjoy breakfast !
1 Like
Local Junior School.
Our local state Junior School has 207 pupils. There are an equal number of pupils in each class. How many classes are there, and how many pupils in each class ?
Widget testing.
As a side-line, I have a small company that manufactures widgets. Each widget needs to be tested prior to customer dispatch. I trialled three widget testers before deciding which one to hire.
Over the one-week trial period, Robert tested twice as many widgets as Steve. Robert also tested four more widgets than Trevor. In total the three widget testers tested 36 widgets between them.
How many widgets did Robert test ?
3 rooms, 69 students.
Nice solution Seakayaker. However …….
Possible (mathematically), but unlikely (educationally).
There are a growing number of schools districts in the US where there is a current lack of funding for the public sector. School systems and other public services are impacted with tax bases decreasing due to a declining population with a higher number of senior citizens. Many are closing schools which impacts families/students needed to be transported to schools further from home. School teachers, administrators and maintenance workers are also losing jobs. So we may be heading back to larger class sizes.
Interesting times ahead… Now back to ‘Brain Teasers’
1 Like
…then you are looking for 9 rooms and 23 students.
2 Likes
Or 69 rooms with 3 students each 
1 Like
I get Robert at 16, Trevor at 12 and Steve at 8.
I’m going out on a limb a say one class of 207 pupils
2 Likes