Elva

"Take sixty-three," Elva said. "Pull the two digits apart and leave a gap: six... three. Now add the two neighbours — six plus three is nine — and drop that nine into the gap. Six, nine, three. Six hundred ninety-three. That's eleven times sixty-three." Elva spread their hands like a magician showing an empty palm. "The outside digits stay where they are, and their sum moves into the space between them. That's the whole trick."

"It works," Elva said, "because eleven is ten and one. Multiplying by ten shifts a number one place left, and adding one more copy of the number lines up each digit with its neighbour — so every middle digit becomes the sum of the two beside it. You don't have to know why to enjoy it, but that's the reason the neighbours add up. The one thing to watch: if two neighbours add to more than nine, the extra one carries left, like a little overflow. Twenty-eight times eleven — two, then two-plus-eight is ten, so write the zero and carry the one to the two: three, zero, eight. Three hundred eight. Even the carry is gentle."

The student tried 11 × 45. "Four... five. Neighbours: four plus five is nine. Drop it in: four, nine, five. Four hundred ninety-five." They laughed out loud. "That's it? I didn't multiply anything!" Elva nodded, delighted. "You added once. Now try one that carries — eleven times fifty-seven. Five and seven, gap between. Five plus seven is twelve — write the two, carry the one to the five: six, two, seven. Six hundred twenty-seven." The student did it and beamed. "Six hundred twenty-seven. The carry just nudged the front digit up. That's almost cheating."