Here are a few excerpts from different dictionaries concerning the matter of question:
give (someone) a run for their money
- to challenge, to arrange someone complexity
We were going to give the rival team a run for their money during the competitions.
give someone a (good) run for one's money
1. to give one what one deserves, expects, or wants - worth the (money, labor, effort, and expectations), cost of money paid; ~ bring somebody pleasure for its money
2. somebody. run, worried, and so n; ≅ pan; ≅ show where what's what
Example 1: Give them a run for their money. - ... Ask them to heat, show them where what.
Example 2: I'll give him a run for his money. - I am going to ask him, I'll show him, and I tick him off, I will give him what for. I will give him a
Have a (good) one's run for money - to have fun (for my money, the works); ≅ not in vain to try; ≅ have an impact
Student or Learner