It’s gotta be the shoes, the students told one another.

The four Blaine High School seniors holding a brainstorming session at a ­Caribou Coffee shop had exhausted every possible idea for their Center for Engineering, ­Mathematics and Science (CEMS) project. They were nearly sold on attempting to invent a toaster that, when flipped sideways, makes grilled cheese sandwiches.

Then it hit them.

They noticed the athletic shoes that teammate Andy Nelson was wearing. At the toe of one shoe, the sole had separated. With each step, the sole would awkwardly catch the floor, nearly turning Nelson’s ankle.

“Andy,” said Shilvi Joshi, “you need new shoes.”

But instead of buying a new pair, why not just replace the sole? Hey, if the idea fits …

Students at CEMS, a Blaine magnet program that draws from eight school districts, have generated enough ideas to earn a collective $1 million in college scholarships over the past two years, said Dr. Lori Dykstra, curriculum integrator at Blaine High School. The kids, all of whom will receive diplomas from Blaine, come from as far away as Zimmerman, Hanover, Rockford and Buffalo.

They’re smart, curious and creative — and, in many cases, very well-rounded. Chris Zins, a senior from Coon Rapids who plans to major in engineering at the University of Minnesota, is an Eagle Scout. Antoinette Zoumenigui, another senior from Coon Rapids who plans to study molecular biology at the University of Minnesota, or possibly the University of Pennsylvania, is a star high jumper on the track team. Shilvi Joshi of Blaine hopes to study bio-medical engineering or go into pre-med; she was accepted at Minnesota, but is still waiting to hear from Brown, the University of California, Boston College and Washington University. She made it to a national competition for her debate skills.

Shoes weren’t the sole idea

Last week, at an assembly at Blaine High, 70 future mathematicians, engineers and scientists showcased their original projects.

There was a bicycle light with power generated by the friction coming from nine magnets attached to the spokes of the rear wheel. There was a thermostat designed for a space suit — to keep the wearer cool.

And the foursome of Logan Wendt, Zoumenigui, Joshi and Nelson introduced to the public what very well could be the first athletic shoes with removable soles. The soles are attached to the base of the shoes by a zipper that outlines the shoe. When the sole is worn down, just unzip it and zip on a new one.

“We wanted to come up with a problem and a solution that would help society,” Shilvi said. “I used to play basketball as a freshman. The treads on my shoes constantly wore down. Why buy new shoes if all you need to change are the soles?”

It sounded more practical than inventing a device that would automatically lock bathroom doors until hands were washed — an idea Wendt proposed.

Many ideas, limited budget

There was no limit to the variety of ideas, but there were budget limitations for each project. The CEMS program received a $1.5 million grant, spread over three years, that covers transportation for students, a double-room equipped with computers and lab equipment, and other curriculum costs.

For last week’s assembly projects, each group of three to five students could spend up to $500 on materials, but no more, Dykstra said. The shoe project cost about $120 for materials — which involved buying zippers and two pairs of New Balance athletic shoes.

The bicycle light was more expensive. It required the nine magnets with 120-pound pull force that were inserted into brackets the students designed. There were coils that the magnets pass as the rear wheel spins — inducing an electric charge that runs through wires to a battery mounted to the bicycle frame. And there is the light itself.

“I’d been telling my brother that it would be nice to charge your phone while riding a bike, and you could do this with this electrical system we’ve created,” said Nick Lindberg, who worked on the project with Zins, Ian Hamliton, Jonathan Nguyen and Christian Vasquez. (All hope to attend the University of Minnesota this fall.)

The students know that a generator light that costs nearly $200 to create might not be practical. The magnetic holding brackets, which the students designed on computers, had to be specially made. But costs could be drastically reduced once a mold was made, they said.

“It works,” said Nguyen. “That was the most important thing.”

Bethany Bartko, who will study either engineering at the University of Minnesota or nursing at Winona State next fall, was a member of a team that designed the thermally cooled space suit. She said the team got the idea after talking to their science teacher, John Bayer. As a member of the National Guard, Bayer, a bioengineer, wears a suit that becomes “super hot,” said Bartko.

“We took a cooling unit out of the fridge,” she said, crediting teammate Jacob Arntzen with the idea. “You can pack it on your back and it can cool down or heat up. “It needs tweaking, but we think it will work.”