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Gardner, who died in 2010, wrote “Undiluted Hocus-Pocus” at the age of 95 in a one-room assisted-living apartment in Norman, Okla. He worked on an old electric typewriter and edited with scissors and rubber cement as he stood at the lectern from which he had long addressed the world in print. “I am given five pills every morning after breakfast,” he writes. “My blood pressure is low, my cholesterol is so-so, and my vision is perfect.” But, he adds, “at 95 I still have enough wits to keep writing.”

Gardner was a child of faith and skepticism. His mother was “a devout Methodist”; his father, a Scripture-doubting science buff, a wildcatter who built a career on oil. When his mother spotted a rainbow, “she would hurry to the phone and call a dozen friends, urging them to go outside” and see the miracle. His father explained the rainbow’s optics and built Martin a science lab next to the kitchen.

“The wonderful thing about a rainbow,” Gardner writes, “is that it is not something ‘out there’ in the sky. It exists only on the retinas of eyes or on photographic film. Your image in a mirror is similar. It’s not a thing behind the looking glass. By the way, what does a mirror look like when there’s no one in the room? And why does a mirror reverse left and right but not up and down?” “Undiluted Hocus-Pocus” is full of such challenges, teasing the reader in a warm, friendly way, like a sly uncle.