From Diane Resek, Professor Emerita of Math, San Francisco State University
This problem was adapted from a problem in A Think Twice Quiz for a Cold Night by Harold Taylor, California Math Council, Northern Section, 1969.
Take the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 and arrange them in any order to make two numbers in two rows. Now add the two numbers to get a third row.
Find one or more arrangements in which each of the ten digits is used once and only once in one of the three rows.
If your students get stuck, try adding more constraints (problem from nrich.maths.org/804):
This addition sum uses all ten digits 0, 1, 2 ... 9 exactly once. Find the sum and show that the one you give is the only possibility.
| * | * | 4 | |
| + | 2 | 8 | * |
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| * | * | * | * |
There are several other interesting puzzles with a similar name involving ten-digit numbers, e.g., Write a ten-digit number where the first digit indicates the number of zeros in the ten-digit number; the second digit the total number of ones; the third digit the total number of twos; and so on until the last digit, which indicates the total number of nines. For example, 8000000010 is not true because there is one 1 but the second digit is 0, not 1. (mathforum.org/library/drmath/view/65585.html).
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