Is an offer to pay a fixed sum upon hitting a target with an arrow valid as a contractual wage (Ja'alah)?

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The contract where a man tells another, 'Shoot this arrow; if you hit the target, you will have one dirham,' is valid and constitutes a wage agreement (Ja'alah). This is because a sum of money is offered in exchange for an act that has a legitimate purpose for the offeror. This scenario does not constitute a contest of archery (Nidhal), as Nidhal requires participation by two or more parties who all shoot, and the prize goes to the one who prevails.