A Fistful of Brain Teasers
Posted by: Don Atkinson on 13 November 2017
A Fistful of Brain Teasers
For those who are either non-British, or under the age of 65………. The UK used to have a brilliant system of currency referred to as “Pounds, Shillings and Pence”. Simplified to £ ״ s ״ d. No! Don’t ask me why the “Pence” symbol is a “d”, just learn it and remember it !
A £ comprised 20 Shillings and a Shilling comprised 12 Pence. Thus a £ comprised 240 Pence. I reckon that both Microsoft and Apple would have difficulty with these numbers in their spreadsheets, more so if we included Guineas, Crowns, Half-Crowns and Florins. However, I digress..............
The purpose of the explanation is to assist with the first two or three teasers that follow. So just to ensure a reasonable comprehension has been grasped…. ….. if each of three children has £3 − 7s − 9d, then collectively they have £10 − 3s − 3d Got the idea ? Good ! Just try 5 children, two each with £4 − 15s − 8d and three each with £3 − 3s − 4d. How much do they have between them ? (this isn’t the first brain teaser, just the basic introduction with some “homework”, the Teasers follow)
The Suttons are 13,14,34,39 and the Suttcliffs are 8,10,40,42.
Regarding the Suttons:- If the youngest child is "a", the oldest child is "a+1". If the mother is "x", and the father is "y", then y = 100 - (2a+1+x). So, 4 ages have only 2 variables. Similarly for the Suttcliffs.
I could get to a fairly clumsy formula, but could only find the solutions by even clumsier Excel trial and error. Knowing Don, I'm sure there must be a nicer solution.......
How many triangles can be determined in the above diagram ?
Hi Don,
at least fourteen, but I will keep looking for more 
Mulberry posted:Hi Don,
at least fourteen, but I will keep looking for more
Good shout ! ie "I will keep looking for more" 
Christopher_M posted:16
Hi Chris, nice try but.............
...................same advice that I proffered to Mulberry............
Remember, there are triangles within triangles etc eg, the two triangles below the bottom horizontal line together make a third triangle
Ignore the first picture (top left) - it's just a reminder of the puzzle.
The other five show some of the triangles.
Next post will show the rest.
...........and this slide shows the rest !
So now it's just a case of counting the shaded triangle and making sure there are no omissions and no duplications !
Just make sure you count carefully !
Start anywhere on the top row.
Move through the grid from one connected box to another.
Finnish on the bottom row.
Your total must add up to 100.
What is your route ?
Arithmetic Squares !
In this puzzle, you place the numbers 1 thru 9 in the empty boxes such that the equations/relationships are correct, both vertically and horizontally.
You only use each number once.
The sums are progressed Left to Right and Top to Bottom
Youignore the usual precedence rules
I have illustrated the concept with an example in the post above !
Odd Ball?
I have twelve balls that LOOK identical but one (and only one) is either heavier or lighter than the rest.
Using a pair of scales, I can compare the weight of any combination of balls that I chose. What is the MINIMUM number of weighings that I need to make, in order to identify the odd ball and decide whether it is heavy or light?
PS 'scales' = those old fashioned ones that look a bit like the Scales of Justice. Foe example, I could put three balls on each side and if they balanced, I would know that the odd ball was not one of those six. And that would be ONE weighing gone