Education The Garden Of The Sphinx

...anyone ever come across this book? I've recently been geeking out over how fantastic it is. It's a book of small somewhat-mathematical brain teasers that encourage lateral thinking, logic and inventive problem-solving.

The first problem in the book, as an example:

My old maths teacher used to do one of these over breakfast every morning to "keep in shape" They take me considerably longer.

 

Simple. The desert is the Arctic desert (since desert, by definition, is a dry, arid region, not necessarily hot). You can survive off melting snow. ;-)

 

Go alone, plant the flag. Have a friend meet you on your return on the 5th day and give you their spare water. Another friend turns up the next day and so on until you are all out of the desert.

I haven't come across the book, but we used to have a board game called (iir) Mindgames or something, which had a collection of cards with different puzzles on them. I was no good at it.

 

This is the logical inverse of the normal solution, but it would work. The conventional method is to have all 4 men set out, then at the 1, 2 and 3 day marks send one back each time, giving his spare water to the remaining men. Mathematically it amounts to the same thing.

edit - although it does have a logistical weakness. The conventional method has a small error margin - unless a man dies or something, you're going to get there. The inverse method relies on the remaining men leaving on time after you've departed, and being synchronised without being in contact, which is quite a leap of faith.

 

If you're applying reality to the question, then yes, it does become more complex. But then if you plan on walking four days into a desert you can assume people would all own watches, maps and compasses. I figured it would be like air-to-air refuelling, and if something really does go wrong, they can send the Land Rover.

 

Another fun one designed to illustrate the value of pure logic as opposed to relying exclusively on advanced maths to solve problems, this problem requires nothing above primary school maths and a bit of lateral thinking:

 

Basic speed:

380 / 26 = 14 8/13 m/s (keeping it exact as a fraction, to use in part 2)

Length:

(380 * 7) / 26 = 102.3m (give or take 1/2mm)

Lateral thinking tells me the train would stop at the station. But maybe I'm being silly.

 

I would take less food and more water as i could easily survive a few days without food but not without water.

 

Like my flatmate, you've made it more complicated than it is meant to be by taking 'traverse' to mean one point on the train going 380 metres. In fact, to traverse it means from the front of the train hitting the beginning of the platform to the end of the train passing the end of the platform.

This is why I drew attention to the fact that it only requires primary school maths. And a bit of mental visualising.

edit - there is no food involved in the desert one for the sake of simplicity. If it were a fully realised scenario we'd have to start going into toilet breaks and cardiovascular fitness

These really aren't going down well. I wonder whether they were simply written for another generation's way of thinking.

 

If to move one length the train takes 7 second then it move's a 7th of its length so in 26s it will move 26/7 lengths so the station is 19/7 train lengths so the train is 380*7/19 metres long.

 

Simple. You take a 5 day supply and one companion, who also has a five day supply. You drink his water, leaving him to die at the end of the third day. That way you are three days in, with one day forward and four days back to go - meaning a total journey of five days - while still carrying five days worth of water.

Spoiler

Or, you assume you can drink at camp on the first day. Then, you take one companion. Second day, you both drink X's water, leaving him two days in and with two days water left to get home with, which is possible. That leaves you on your third day in with five days worth of water still - one for the journey forwards (to reach the destination) and four left for the four days return journey.

Time for Einstein's Riddle, methinks.

Supposedly Einstein took two weeks to solve it and said 98 per cent of people would be unable to do so.

 

/snip/ - That's a horrible riddle, horrible horrible horrible.


Here's how to do it mind, Uber tips

 

You can't just drink ten litres of water before you leave and slosh your way through the first day. That's cheating.

edit -
Einstein's 98% claim is probably apocryphal and even if it isn't, it should be treated with a patronising pat on the shoulder to him given that he was a clerk, not a sociologist, psychologist or anthropologist. I'd disregard population statistics invented by a man who only had regular contact with a couple of human beings and dismissed the majority of the race as too stupid to bother with.

 

What about:

Day 1 - send everyone packing to safety, drink 15 days' worth of water immediately.
Day 2 - survive off your own wee.

And so on?

EDIT: You'd still have your 5 days of water to top off the tank, so to speak.

 

Purifying your own urine to a point where it is safely consumable is surprisingly easy, not that I have ever been in a situation where that is nessecary nor ever done it..

IIRC, two plastic bottles, stick with the bottle necks touching and facing each other so that the open tops are together, urinate into one (before placing them together) about half way full, place them as aforementioned in the sand and cover the one filled with urine in sand, leave for a few hours, the other bottle has water in it! magic!

 

If you're desperate you can just drink the urine straight. I think you get bad buildups of....something or other after a while, though, so it's not recommended.

Anyway this is a thoroughly irregular non-solution! You are NOT allowed to drink several gallons of water before leaving, nor would it be very medically commendable to do so.

The test assumes you have a normal-sized, human bladder.