From the Super Mario Wiki
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In the original Nintendo 64 release, every course has a Silver Coin Challenge, where the player's objective is to collect eight Silver Coins and win in first place. Many of the Silver Coins are well hidden or located off-track. The player can only participate in a world's Silver Coin Challenges after winning against the world boss in a race, and by having enough Golden Balloons to re-enter the respective courses. After completing a Silver Coin Challenge, the player wins a Golden Balloon.
In Diddy Kong Racing DS, the Silver Coin Challenges are all replaced with Balloon Touch Challenges in Adventure Mode. The Silver Coin Challenges still exist in the single race mode, and can be purchased from Taj's wish menu. Each track's Silver Coin Challenge must be unlocked by completing its respective Balloon Touch Challenge.