Balancing the state budget is more than a math problem. That fact is being pressed hard on the three major-party candidates for governor, who have been called upon almost daily for the past several months to explain how they would erase a projected $5.8 billion deficit in 2012-13.

Last week, DFL gubernatorial candidate Mark Dayton amended his proposal, acknowledging that his first attempt did not add up to a balanced budget. The second one doesn't, either. Dayton acknowledges a remaining $890 million gap. Perhaps unwittingly, he is demonstrating that the hole in the state budget is too big to fill with a "tax the rich" strategy alone.

The former U.S. senator was cum laude at Yale University and was once a high school science teacher. His math skills are not in doubt. His trouble lies in finding sufficient budget adjustments that are in keeping with his promises to spare all but upper-income Minnesotans from higher taxes, while increasing education spending at the same time.

Dayton is to be commended for submitting his tax-raising ideas to the rigors of Department of Revenue analysis. It found that his initial surmises about the revenue his proposed new income tax bracket for the state's top earners would raise were nearly $2 billion too optimistic. (The Independence Party's Tom Horner said Friday that he has done the same with his proposals for a broader-based sales tax and elimination of some income-tax deductions and exclusions. He should release the department's analysis.)

Some of the revenue-raisers Dayton added to his budget plan last week seem similarly grounded in wishful thinking. For example, it's not likely that a crackdown on tax cheaters would net nearly $340 million a biennium, or that Minnesota can unilaterally change the way two-state "snowbirds" define their residency for income-tax purposes. The state of Arizona, for one, may have something to say about that.

Dayton should also rethink some of the items on his list of spending cuts. His intention to save $425 million a biennium by reducing outside contracting of state work sounds far-fetched, and may be ill-advised. Much of the contracting state government does purchases specialized skills, such as highway and transit engineering, that would be expensive to acquire in-house and that save taxpayers money in the long run.

He's also underestimating the value of the Minnesota Trade Office, which was founded in 1983 by Dayton's old boss and mentor, the late Gov. Rudy Perpich. Dayton argued that the trade office's work could be moved to the governor's office, for a $3 million savings. But that savings would only materialize at the sacrifice of some of the valuable day-to-day assistance the office supplies to Minnesota companies seeking overseas buyers for their goods and services. It's no accident that exports from Minnesota did not drop as much as in most other states during the Great Recession, and are up 18 percent in the first half of 2010 -- nearly back to prerecession levels.

In announcing such specific spending ideas before the election, Dayton is taking a risk -- one that should be emulated by Horner and Republican Tom Emmer.

Each of the three leading candidates boasts that he is offering the most detailed plan to balance the budget. In fact, each plan leaves a considerable amount to the imagination. For example, Horner seeks to apply the state sales tax to an array of as-yet-unspecified consumer services, and wants to derive more than $1 billion in savings via as-yet-unspecified government "redesign."

Emmer is guilty of treating the budget exercise as merely a math problem. He has proposed spending limits in five categories that add up to the $33 billion the state is projected to collect in 2012-13 if no tax is increased. But he hasn't described how higher education, or cities and counties, or sick and needy Minnesotans will be affected by the nearly $6 billion in program changes that will be required to meet his spending targets. If he won't, it behooves the Minnesotans who would be ill-served by those changes to educate their fellow citizens about what is at stake in Emmer's proposal.

These three candidates are fond of congratulating themselves for revealing more to voters about their intentions than any previous contenders for the state's highest office. They may be right. But the dire fiscal circumstances in which state and local governments find themselves this year demand more disclosure than usual of those who seek to lead government back to solvency and the state to prosperity. The candidates for governor should expect questions about how they would get Minnesota out of the ditch to just keep coming.