### 743403 is he dead

Listen carefully and then tell us a secret about yourself. dbcghajghb

This is a mathematical poem from India. It's quite easy to solve once you get the hang of it :-

O beautiful maiden with beaming eyes, tell me,

Since you understand the method of inversion,

What number multiplied by 2,

Then increased by three quarters of the product,

Then divided by seven,

Then diminished by one third of the result,

Then multiplied by itself,

Then diminished by 52,

Whose square root is then extracted,

Before 8 is added and then divided by 10,

Gives the final result of 2?

Answers in the comments. :)

Suppose that you have access to an 11-gallon container, a 6-gallon container, and a source of running water (such as a water tap). You do not have access to any measuring devices, but you are allowed to pour water down a drain.

How would you set about measuring out 8 gallons of water?

Answers in the comments please. Another puzzle in about a week.

You have 3 containers, labelled A, B and C.

Container A has a capacity of 8 litres; container B has a capacity of 5 litres; container C has a capacity of 3 litres.

Currently, container A is full to the brim with water, whereas B and C are empty.

You are allowed to transfer water from any one container to the other, but are not allowed to use external water sources such as taps (so no pouring water down the drain and re-filling). You have no access to measuring equipment, and you are not allowed to 'guesstimate' water levels by eye (so, for instance, you cannot pour water from A to B and then do a visual check that they are approximately the same level, or 'half full').

What steps do you need to take to get to a state where 4 litres of water are in A, 4 litres of water are in B, and C is empty?

Two walkers spend from 3 pm until 9 pm walking along a level road, walking up a hill, and reversing their steps down the hill and back along the level road to return back home again. Their pace on the level is 4 mph, uphill 3mph, and downhill 6 mph.

How far did they walk?

To the nearest half hour, at what time did they reach the top of the hill?

Answers in the comments please.

The next puzzle will about a week from when this one was published!

Three puzzle competitors are blindfolded. A white piece of paper is glued to each competitor's forehead and they are told that not all of the pieces of paper are black. The blindfolds are removed and the competitors are told that the prize will go to the first to deduce whether the paper on his forehead is black or white.

The three competitors are silent for a short time, then all three announce white at the same time. Why?

Answers in the comments please. Note that there are two possible answers to this one - one relatively easy and intuitive, one harder and more 'logical'.