Take two Students, each one of them solved 3 problems in one contest with following time:

Student 1: Q1: 10min, Q2: 50min, Q3: 10min in this order

Student 2: Q1: 15min, Q3: 15min, Q2: 60min in this order

Which one of them, do you think deserve the better rank? I think 1st student.

But the scheme here used computes the sum of the time taken to solve each problem from the start of the contest.

Since,

Total time for student 1: 140min (10+60+70)

Total time for student 2: 135min (15+30+90).

So, this way Student 2 gets the higher rank.

I could not find any benefit of this scheme, other then this is used in ACM ICPC.

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You are ignoring the aspect that the better candidate should be able to identify which question to tackle first, which means that they should be able to at the very least get a little idea of what concepts the question could finally narrow down to and what question could be solved faster than the other, since every question is available from the start.

If the first student solved the questions in order of Q1->Q3->Q2, he would have a higher rank.

If the second student solved the questions in order of Q3->Q1->Q2, he would have a lower rank.

Problem Solving in a contest or even in real life is not just “How To Do”, but also “What To Do” and “When To Do”. Smart Work quite often beats Hard Work.

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