Math Puzzle: Comply with the Calculator Clues
An previous calculator makes use of a seven-segment show, during which numerals are represented by completely different patterns of vertical and horizontal line segments. However the gadget is defective and not exhibits any vertical segments. Somebody sorts a quantity into this calculator, and the show exhibits the horizontal segments seen within the prime picture. Subsequent the individual presses the multiplication key and kinds in a second quantity. The show now exhibits the horizontal segments within the center picture. After the person presses the equal key, the show exhibits the horizontal segments within the backside picture. Which two numbers have been multiplied with the calculator?
The final digit of the product have to be 7. As a result of the final digits of the 2 components may be solely 2, 3, 5, 6, 8 or 9, one issue should finish in 3 and the opposite in 9. The tens digit of the primary issue may be solely 4. Thus, the product could possibly be 49 × 3 = 147 or 43 × 9 = 387. However the first risk is dominated out as a result of the a whole lot and tens digits of the product may be solely 2, 3, 5, 6, 8 or 9—leaving us with the second resolution.
All three numbers can, nevertheless, nonetheless have a number one 1 that will be invisible. With a most of 1 main 1 per quantity, there are three extra attainable options: 143 × 9 = 1,287, 49 × 13 = 637 and 149 × 13 = 1,937. It’s straightforward to verify that for all components with a couple of main 1, the product doesn’t consist fully of 1’s aside from the three ultimate digits.
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This puzzle initially appeared in Spektrum der Wissenschaft and was reproduced with permission.
