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)
Ian G. posted:Don Atkinson posted:Dozey posted:I see 11.
Same here. 5 + 4 + 2 = 11
Just waiting for someone to identify more..........I'd be surprised, but you never know !
Yep I only see 11.
11 it is then !! 
How many triangles are there in this figure ?
Don Atkinson posted:
Looking at things from different angles is all well and good, but sometimes a sense of direction is needed !
48 degrees, calculated as follows;
By extending the non-parallel line (ie that has a 32 deg angle) to the lower parallel line, a transversal line is created where the lower parallel is cut, thereby creating a corresponding angle of 32 deg. The transversal line also creates a straight line angle of 180-80 = 100. The transversal line also creates a triangle. There are 180 degrees in a triangle. Therefore angle B = (180-(100+32) = 48 degrees.
Don Atkinson posted:
How many triangles are there in this figure ?
I think 20 ...
ynwa250505 posted:Don Atkinson posted:
How many triangles are there in this figure ?
I think 20 ...
Yep, looks like you, Ian and myself are all in agreement. 20 ! (that's 20. NOT 20!)
Remember, these are all abstracts from my O-Level maths book. This was a "puzzle" and the book never provided answers to the "puzzles". It did provide answers to the progress test questions - such as the "Angles" questions !
ynwa250505 posted:Don Atkinson posted:
Looking at things from different angles is all well and good, but sometimes a sense of direction is needed !
48 degrees, calculated as follows;
By extending the non-parallel line (ie that has a 32 deg angle) to the lower parallel line, a transversal line is created where the lower parallel is cut, thereby creating a corresponding angle of 32 deg. The transversal line also creates a straight line angle of 180-80 = 100. The transversal line also creates a triangle. There are 180 degrees in a triangle. Therefore angle B = (180-(100+32) = 48 degrees.
Yep, 48 degrees. I did it a different way, but nothing wrong with yours.
I drew a third parallel line, passing through the apex of angle 80 deg.
Then using the "Alternate Angle Theorem" the top part of 80 deg is 32 deg and by subtraction (80 - 32) the bottom part of the 80 deg angle is 48 deg.
Using the "Alternate Angle Theorem" again, in the bottom part of the drawing, gives b = 48 deg
ynwa250505 posted:Don Atkinson posted:
Looking at things from different angles is all well and good, but sometimes a sense of direction is needed !
48 degrees, calculated as follows;
By extending the non-parallel line (ie that has a 32 deg angle) to the lower parallel line, a transversal line is created where the lower parallel is cut, thereby creating a corresponding angle of 32 deg. The transversal line also creates a straight line angle of 180-80 = 100. The transversal line also creates a triangle. There are 180 degrees in a triangle. Therefore angle B = (180-(100+32) = 48 degrees.
Yes, or 80 - 32 = 48. The two angles on the outer lines will always add up to the inner angle.
Don Atkinson posted:
I thought I posted before. I think 17 & 6.