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Students from Jack Hunt School Peterborough called this "the blank boxes puzzle" and sent lots of good solutions including some beautifully word processed work:
64 x 58 = 3712 (Kenny) 37 x 58 = 2146 (Daniel) 24 x 57 = 1368 (Adnan) 34 x 52 = 1768 (Freddie)
James, Sheherazade, Nicola and Elizabeth from Jack Hunt School, Peterboroughand Larissa, Hollie, Emma, Emma, Laura, and Lyndsay from The Mount School, York all gave excellent explanations of how to use logical thinking and be systematic in searching for solutions.
James provided a diagram highlighting the pairs of numbers he could eliminate according to the following rules. James reduced the number of cases he had to check by multiplication and found the four solutions given above. In his diagram all the numbers from 23 to 87 are included and the cells are coloured in as the number pairs are eliminated.
Beth from The Mount School, York found two solutions for the numbers 2 to 9:
53 x 92=4876 62 x 87=5394
Are there any others? Are there any solutions for digits 0 to 7?