An old calculator uses a screen of seven segments, in which different models of vertical and horizontal line segments are represented. But the device is defective and does not show a vertical segment. Someone calculates a number in this calculator, and the screen shows the horizontal segments visible in the image above. Then press the key to multiplying people and presses the types in a second number. On the screen now shows horizontal segments in the middle image. After the user press the same key, the screen shows the horizontal segments in the image below. Which two numbers were multiplied with the calculator?
The last digit of the product must be 7. Because the last digits of two factors can be 2, 3, 5, 6, 8, 8, a factor must complete the 3 and the other. The first factor in the Tens digit can be only 4. Thus, the product could be 49 × 3 = 147 or 43 × 9 = 387. But first option leaves us with hundreds of products and tens of digits only 2, 3, 5, 6, 8 or 9-second solution.
Three numbers, however, can still be a leader that would still be invisible. Up to 1 per number, there are several more solutions: 143 × 9 = 1.287, 49 × 13 = 637 and 149 × 139 = 1,937. It is easy to check for all factors with more than 1 point, the product is not completely separated from the last three digits of 1.
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This puzzle originally appeared Science spectrum and reproduced with permission.
