PHOENIX — Patrick Byrne, a 42-year-old bear of a man who bristles with ideas that have made him rich and restless, has an idea that can provide a new desktop computer for every student in America without costing taxpayers a new nickel. Or it could provide 300,000 new $40,000-a-year teachers without any increase in taxes. His idea — call it The 65 Percent Solution — is politically delicious because it unites parents, taxpayers and teachers while, he hopes, sowing dissension in the ranks of the teachers unions, which he considers the principal institutional impediment to improving primary and secondary education.

The idea, which will face its first referendum in Arizona, is to require that 65 percent of every school district's education operational budget be spent on classroom instruction. On, that is, teachers and pupils, not bureaucracy.

Nationally, 61.5 percent of education operational budgets reaches the classrooms. Why make a fuss about 3.5 percent? Because it amounts to $13 billion. Only four states (Utah, Tennessee, New York, Maine) spend at least 65 percent of their budgets in classrooms. Fifteen states spend less than 60 percent. The worst jurisdiction — Washington, D.C., of course — spends less than 50 percent.

Under the 65 percent rule, Arizona, which spends 56.8 percent in classrooms, could use its $451 million transfer to classrooms to buy 1.5 million computers or to hire 11,275 teachers. California (61.7 percent) could use its $1.5 billion transfer to buy 5 million computers or to hire 37,500 teachers. Illinois (59.5 percent) would transfer $906 million to classrooms (3 million computers or 22,650 new teachers). To see how much money would flow into your state's classrooms, go to firstclasseducation.org.

Byrne, who lives in Utah and has made a bundle in various business ventures, was once advised by Warren Buffett to pretend he is a batter at the plate with no one calling balls and strikes, so he can wait for a perfect pitch — a perfect idea. The 65 Percent Solution is perfect because it wins 80-plus percent support in polls and torments people Byrne thinks should be tormented.

Buffett also advised him to ask himself this: If you had a silver bullet, what competitor would you shoot, and why? Byrne says he would shoot the National Education Association — the largest teachers union. Byrne is pugnacious — after graduating from Dartmouth, studying moral philosophy at Cambridge and earning a Stanford doctorate, he tried a boxing career — and relishes the prospect of the 65 percent requirement pitting teachers against other union members who are in the education bureaucracy.