Is paying a weekly sum to three students, with the student who achieves his goal receiving the total amount, considered a form of gambling or religiously problematic?

Gambling is a state of vacillation between profit and loss, and this is realized in student competitions where they fluctuate between gain and penalty, making this competition a form of gambling. If the prize is offered by the Imam or someone else, or by one of the contestants for the winner to take, then the contract is valid and the prize is permissible by the consensus of the jurists. However, if the two contestants contribute the prize for the winner to take it from them, then the competition is not valid and the prize is not permissible, because it is prohibited gambling.