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)
An infinitely large floor is covered with hexagonal tiles side L. Different coloured tiles are used such that no two adjacent tiles are the same colour.
A thin hoop diameter D is thrown onto the floor at random.
What is the probability of the hoop laying across more than one colour of tile ?
You want to be an astronaut ? (as an alternative to popeye's what DO you do ?)
- Box of matches
- Handheld GPS receiver
- 15 metres nylon rope
- Three spare batteries for spacesuit
- Parachute silk
- Three spare carbon-dioxide removal canisters for spacesuit
- One case of dehydrated food
- Three spare oxygen tanks for spacesuit
- Stellar map
- Self-inflating life raft
- Magnetic compass
- 20 litres of water – can be administered through a special drinking port in spacesuit
- Two handheld mirrors
- First-aid kit including medical tape, scissors etc
- Solar-powered FM receiver-transmitter
You and two crew members have crash-landed on the moon 50 km from your intended rendezvous with the Lunar Base. Survival depends on reaching that Lunar Base. Your spacecraft and most of its contents have been destroyed but the most critical items from the above list of undamaged items must now be selected for your journey.
The good new is that in the lunar gravity, you can travel at 5 km/hr. The bad news is that your built-in spacesuit consumables will only last for 8 hours.
Group the above items in order of importance/usefulness for reaching the lunar base. Put them into three groups viz – Essential; Useful; Not much use.
PS it's only a game, there is no risk that you, or any other "middle manager" will be on the next rocket to the moon 
Although the "squares on a chess board" also came out of he O-Level book, I have always seen it as a "Character Assessment" type of question rather than simply a maths question.
Sure, the question as presented is somewhat vague. and It is presented as a "Puzzle", so more for amusement than O-Level progress. Unlike the "proper" questions, there are no answers given at the back of the book for puzzles !
So, 10/10 for all the Character Assassination responses - well done - and i'm sure there are plenty more !
As for IB's second attempt............... well it's along the right lines ...................
Well done IB !
Eventually, 
A starter for 10 for the hoop in a hexagon teaser above.
Probability of hoop spanning more than 1 colour in the hexagonal tiling is
oops 
Note to self: 1 don't try and do more in your head than you can and 2 - sense check your answers!
Ian G. posted:oops
Note to self: 1 don't try and do more in your head than you can and 2 - sense check your answers!
Ah !
Much better and....... much neater into the bargin !! Brilliant