Billboard has been in existence for 116 years. And since 1958, the publication has released its Hot 100, charting the top songs of each week.

Despite such an exhaustive catalog of number one hits to choose from, few of the “American Idol” contestants proved able to find anything listenable when presented with the challenge.

Tuesday’s telecast was a lesson in what not to sing … and how not to sing it. This was made all the more frustrating considering it was the last show before narrowing down the field to ten contestants — a huge deal because those are the amount invited on the summer’s national “Idol” tour. Finally, a chance to quit the day job and make actual money.

Interspersed with peppy teen sensation Miley Cyrus’ “mentoring,” only a few agreeable performances snuck in.

Hippie folk-blues singer Crystal Bowersox occupied the “shooting fish in a barrel category” with her version of Janis Joplin’s “Me and Bobby McGee.” Effective yet unsurprising.

Siobhan Magnus and Lee Dewyze made oddball selections that worked due to their inherent talent: Stevie Wonder’s “Superstition” and The Box Tops’ “The Letter,” respectively. (Magnus is adequately fulfilling the “What will she do next?” role vacated last year by Adam Lambert.)

Aaron Kelly (Aerosmith’s “I Don’t Want to Miss a Thing”) and Michael Lynche (Percy Sledge’s “When a Man Loves a Woman”) belted well-done versions of tunes no one ever needs to hear again.

Then there were the mid-level artists.

Andrew Garcia once again squandered his character-crammed voice with a cruise ship version of Marvin Gaye’s “I Heard It Through the Grapevine.” For the fourth straight week — as the judges accurately pointed out — this guy has no idea who he wants to be.

Similarly, Didi Benami took Linda Ronstadt’s still-cool country-rock hit “You’re No Good” and turned it into a Broadway musical. Blechhh.

Katie Stevens (Fergie’s “Big Girls Don’t Cry”) and Casey James (Huey Lewis and the News’ “The Power of Love”) at least sounded fine. But the tunes came across as straight-up covers. And, come on, Huey Lewis? Really? Of all the number one songs from the past 52 years to choose from. Embarrassing.

And then there were the complete disasters. Hindenburg-style, Dukakis-esque, “Cop Rock”-ian disasters.

Tim Urban was predictably awful, delivering a forced, lackluster rendition of Queen’s inherently gimmicky “Crazy Little Thing Called Love” (ironically, the landmark band’s only number one hit).

But the pretty boy’s rendition was nothing compared to the atrocity unleashed by Paige Miles. While no one was on the edge of their seat waiting to hear a cover of Phil Collins’ “Against All Odds (Take a Look at Me Now),” at the very least it’s a “song” with a “melody.” But sometime between now and three weeks ago, Miles misplaced her ability to sing.

She used to be able to, remember? But now she looks like a glum sorority girl who has been thrown onstage against her will at house karaoke night. Out of breath, out of energy and consistently sharp, flat or in the wrong key, Miles dispensed a routine as uncomfortable as watching that Miss Teen South Carolina speech on YouTube.

If she ends up making the tour, it will be a crime against all humanity.

Bottom three: Tim Urban, Paige Miles and Andrew Garcia.

Going home: Paige Miles. (Arguably the worst performance ever given in the top 12. That even encompasses Kristy Lee Cook.)