Saturday,  February 3, 2001
M I N D  G A M E S

Selfish giant

THERE is a state that is neither solid, nor liquid or gas. In this state lives a selfish giant who has beautiful garden where children love to play in his absence. One day, the giant returns from the other side of the moon when children are playing in this garden of eternal spring. "This is my garden, how dare you enter it without my permission!" says the giant, with such anger that it scares every child out of there.

The giant, then, builds a huge wall around the garden and puts a signboard outside it that reads — "Children who cannot do mathematics should not enter".

Tom Sawyer, eldest of all the kids, reads the sign. He leads a group of children to the giant’s house and knocks at the door. "Kid, go away or I will put you in a bracket and multiply you by zero," the giant shouts. "Sir, we are ready to solve any problem that you give us, but please allow us to play in you garden," says Little Tom for all the kids.


"Ho, ho, ho, is that so? Very well, solve this — I find myself on a railway bridge joining Adland with Badland, 3/8th of the way across from Adland. I hear a train approaching Adland and it is travelling at 80 km per hour. If I run towards Adland, I will meet the train at Adland. If I run towards Badland, the train will overtake me at Badland. How fast can I run?" says the giant. The giant knows that the kids are too young to solve such a problem. Tom Sawyer and his friends do not have the answer. They bow their heads, half in defeat, half in humiliation.

The giant says, "I can run 3/8th of the length of the bridge in the time taken by the train to reach Adland. If I run towards Badland, I will be 3/4th of the way towards Badland when the train arrives at Adland. Therefore, I can run the remaining quarter of the distance from Adland to Badland in the time the train travels the whole distance. Therefore, my speed is a quarter that of the train — 20 km per hour. No more chance for you, now go away."

The spring leaves and winter arrives. It finds a beautiful, but empty garden and decides to stay there forever. Years pass, but spring does not return and the garden remains as frozen as the giant’s heart. He calls up the weather office. "What is the temperature outside? " he says. The weatherman reports that the temperatures at dawn in the past five days have been different each day and that the product of the temperatures is 12. After this, he hangs up the receiver.

The giant is puzzled and calls up the weather office again. "I am too young to solve this problem, please tell me what are the five temperatures?" he says. The weatherman replies that, to find out the five temperatures, the giant needs five different integers, the product of which is 12. The smallest five positive integers (1, 2, 3, 4 and 5) multiply to give 120, so he must use some negative ones. Therefore, the temperatures are -2°C, -1°C, 1°C, 2°C and 3°C. "It is cold outside, which is unusual for this time of the year," says the giant. "The spring says that it will not visit heartless persons who make mathematics a scare for children," says the weatherman and hang up the receiver again.

Just then, the giant sees a little ray of light cutting through the thick fog in his garden. He runs towards its source, where he finds a child under a tree of pearls. The child has tears in his eyes. The giant says, "Sweet child, why do you cry?" The child says, "I have 80 pearls that have fallen off this tree. One is lighter than all the others. If I don’t find the odd pearl in just four weightings, all of these vanish."

The giant says, "Don’t be so disappointed kid, let us try again. Divide the pearls into three groups of 27, 27, and 26. Weigh the first 27 against the second 27. If these balance, then the lighter pearl is in the group of 26. Otherwise, it is in the lighter group of 27. Divide this group of 27 (or 26) into three groups of 9, 9, and 9 (or 8). Weigh one group of 9 against another group of 9. If these balance, then the lighter pearl is in the other group of 9 (or 8). Otherwise, it is in the lighter group of 9. Divide this group into three groups of 3, 3, and 3 (or 2). Weigh one group of three against another group of three. This will narrow the group to 3 (or 2) pearls. We can now determine the lighter pearl with the fourth and final weighing." "Thanks," says the child and vanishes into the fog. The giant realises that light had entered his garden because of the child. He picks up his axe and breaks down the wall and the signboard. "Come children and play, the garden is yours," he calls out.

The spring hears his call, too, and returns to the garden with the children to stay there forever.

— Aditya Rishi