IN THE RACE for mayor, the candidates have been twisting themselves into odd shapes to accomplish two conflicting goals: raising money to help the public schools without raising taxes.

Some people think it can't be done - Mayor Nutter, for one. Nutter recently proposed raising property taxes by 9.4 percent to meet the "ask" by Superintendent William Hite for $103 million in additional city aid this year - and in all years going forward.

The let's-raise-taxes option is out of the question for the men and women seeking to succeed Nutter. At the same time, they know public sentiment is clear: Schools are a big priority. Everyone knows the district needs money. So, they have had to make like Rubberboy and come up with plans - inevitably called "comprehensive" - that add up to the magic figure without using a dime in additional taxes.

The result is a mash-up of ideas, some new, some borrowed, some half-decent, some half-baked. All of them assume that the mayor's office comes equipped with a magic wand to make a reluctant City Council and a suspicious state Legislature suddenly compliant - and only too happy to do whatever the mayor asks.

Collectively, these plans prove that it's not easy to raise a lot of money in a big city without turning the knob labeled "Tax."

By now, we've got enough position papers and public statements to summarize the range of options offered:

Check the Couch for Loose Change. Surely, Anthony Hardy Williams and Jim Kenney argue, there must be enough money lying around in the crevices of city government to come up with money for the schools? So there's $50 million right there.

All of this can be done without "reducing vital city services," Kenney assures us.

It's not as easy as it sounds. After scouring Nutter's recent budget proposal, I could find no line item for "Extra Money Just Sitting Around." Times have been tough; the city budget has barely kept up with inflation. That said, there is a way to extract $50 million from the city budget. It is called RIF: reduction in force (a/k/a layoffs). Lower the complement of city employees by about 400 and you're at the $50 million mark. It's up to the mayor to decide where those RIFs come from. In short, you can do it but don't pretend it won't hurt.

Get Those Delinquents. Get 'em! To the candidates, delinquent taxpayers are Philadelphia's Marcellus Shale: a vast untapped resource sure to yield millions. They want to track these deadbeats down and extract the $550 million in taxes, interest and penalties owed.

First, no one - except maybe Milton Street - is against going after tax delinquents. But there is evidence the well may not be deep. As a Pew Charitable Trusts study recently pointed out, only about 30 percent of delinquent taxes are collectible. The rest of the debts are dust.

Kenney has taken the idea a step further and wants to sell the rights to commercial tax debts to a private collection agency. It's a variation of an idea tried during the Rendell administration, which did not work out at all. Still, Kenney thinks he can sell the rights for about $40 million and send it to the schools.

It would be nice to have that money, but it is a one-and-done. Once you collect it and spend it, there is no more. You can't build a sustainable funding base on it.

Let's say Kenney does sell the liens for $40 million. What happens the next year? Kenney says he will get the additional money from more cuts in the city budget. Which conjures up the image of Mayor Kenney, telling the Fraternal Order of Police, the firefighters and the city employee unions (all of which have endorsed him) that he has no money left to give them raises. "Sorry, guys, I gave it to the schools." Will they be amused? No.

Drink Up Everybody! Is it possible to drink our way out of our problems? Nelson Diaz thinks so. He has an idea to raise $10 million or more by letting bars stay open later than the current 2 a.m. closing time. The longer people drink, the more income from the city's 10 percent across-the-bar drink tax. Councilwoman Blondell Reynolds Brown briefly proposed a similar idea the other year to raise money for the schools.

Community groups, not to mention the police, hated the idea. Rounding up the drunk and disorderly at 2 a.m. is bad enough, but at 4 a.m.? Give us a break.

Diaz would limit his extended-hours idea to what he called the city's "central core." I take that to mean Center City. Since Diaz seems to assume no one actually lives in Center City, it shouldn't be much of a burden at 4 a.m. Doug Oliver has also made noises about this being a good idea. (If the idea comes to pass, both of them should be sentenced to live in an apartment above Dirty Frank's at 13th and Pine streets.)

Sue the S.O.B.s! Lynne Abraham is a lawyer. What do lawyers do? They sue. As her education paper states: "Lynne will fight to make sure Philadelphia gets a fair share of education dollars and will take the State to federal court if they refuse." Any guesses on how long that might take? When it comes to the ticklish issue of school funding, Abraham is good at offering tough statements that, upon examination, are devoid of content. They are like jawbreakers with a cotton-candy center. For example, she demands that City Council step up and step up now and do its part to fund the schools, but doesn't say what it should do. Raise taxes? No, she is against raising taxes.

Here's an idea: Maybe she should sue Nutter for suggesting a tax increase.