SCHOPENHAUER said: "Of all the intellectual faculties, judgment is the last to mature. A child under the age of 15 should confine his or her attention either to subjects like mathematics, in which errors of judgment are impossible, or to subjects in which these are not very dangerous, like languages, natural science, history, etc."

A first-grade student has 100 cards on which the integers from 1 to 100 are written. He also has an unlimited number of cards with symbols "+" and "=". What maximum number of true equalities can be obtained using these cards, if each card is used no more than once? It seems to be an easy delivery to face first up, but everyone who has sent in the solution has dragged it into the stumps. God knows why Tendulkars of the world fail on pitches where debutants score centuries.

Since, for each equality, we use at least 3 cards with numbers, it is impossible to obtain more than 33 equalities. One such set of 33 equalities can be as follows: 1+75=76; 3+74=77; 5+73=78; ... 49+51=100; 24+26=50; 20+28=48; 16+30=46; . 8+43=42;. 4+6=10; 14+22=36. One number, meaning one number card, will remain unused (try 18). Charanpal Singh says that the answer to the problem 'Problem Child' is 20 equalities. There is a method to find prime numbers, called Sieve of Eratosthenes, which he has used to find out the true equalities.

The sieve he has given is a grid of numbers from 1 to 100 arranged in ascending order from top left to bottom right in rows of 10s. There are, thus, 10 rows and 10 columns in this grid. This is how Charanpal describes his method: "In the grid, strike out the numbers 1+2=3, so that, one true equality is obtained. Now, strike out the numbers 4+5=9, so that, the numbers of true equalities is 2. Then, strike out 6+7=13, making the numbers of true equalities 3. Proceeding in this way, we can find that the numbers of true equalities are 20." However, even the sieve gives the answer to be 33 true equalities and it is not difficult to see why; try again, Mr Charanpal.

Arya Sunil obtained his 20 equalities by writing 1 to 100 on paper and using tally bars to calculate the answer. Even then, the solution should be 33 equalities. "The maximum number of true equalities is 49," says Vishal Jindal. Using each card only once, it will be quite an impossible feat to achieve. A problem, which a child could solve, thus, puzzled everyone. It is like getting clean bowled on a full toss in cricket, or failing to put a spot kick into an empty goal in football. Lack of concentration, perhaps. Catches win matches; this one is long lost. Write at The Tribune or adityarishi99@yahoo.co.in. Next week, we unmask Batman and see whether he (or she) is able to save Robin from the Riddler or not.

— Aditya Rishi