"The madman has escaped," says the asylum guard to the dictator who rules with an ice-cold heart. "He will try to enter the caves; find him before he finds the cavemen and bring him to me — alive," says the dictator. This is a land of two laws — one for the rich and the other for the poor. The rich have their houses on hilltops that are too cold for comfort, whereas, the poor live in underground caves that are hot as hell. The light of education that shines bright on the mountains has never entered the caves. The rich have never come down to the caves and the poor do no have opportunities to move up in life because they are uneducated, so, people remain where they are.

In the land of the educated, there is a person who once dared to wander into the poor man’s hell and understood the misery of those who lived there. However, dictator got him arrested and threw him into a mental asylum because the rebel wanted to lead cavemen from darkness to light. "He entered the caves," a guard reports to the dictator. "This is the beginning of the end," says the dictator and sinks into his chair.

Meanwhile, the madman is held captive by the cavemen, some of whom recognise him as the man who visited them once and take him to their chief. "Are you the deliverer?" says the chief on seeing the madman. "The deliverer?" says the man. The chief says, "All chiefs pass on a secret to the next chief — that there shall be a deliverer who will lead us from darkness to light." "How can the deliverer be recognised?" says the man. "The dictator has an ice cube and our houses can be in the hills only if that cube melts. To melt the cube, you have to place the numbers 1-8 at the corners of the cube, such that the sum of the four digits on each face is the same. Only the deliverer can do that," says the chief.

a-----b

/: /|

/ : / |

d-----c |

| h....|..g

| / | /

|/ |/

e-----f

"I think I can do that," says the deliverer, "but I need your support." The madman spends years in teaching the cavemen and education transforms them so much that when they knock on the doors of the hill kingdom, the guards let them pass. "I can solve your ice-cube puzzle, but I shall let my friend from the caves have the honour," says the madman to the dictator. The dictator is sure that a caveman cannot crack the puzzle, so he lets the chief make an attempt, who solves it as under:

1-----4

/: /|

/ : / |

8-----5 |

| 7....|..6

| / | /

|/ |/

2-----3

Face sum = 18; "Ignoring any reductions due to symmetry, there are 144 equi-sum-faced cubes out of 40,320 cubes for (a-h)=(1-8) and only three unique cubes," says the chief as the cube and the dictator’s heart melt, after which, warmth returns to hills and light to the caves. "How did I do it? You were the deliverer," says the chief to the madman, who says, "Each of us is a deliverer; so, each one teach one."

— Aditya Rishi