Comments for Digital Substitute https://shawnurban.wordpress.com Teaching should inspire curiosity, provoke thinking, provide context and dole out details. Actually, the emphasis should be done in that order. Sun, 15 Dec 2019 20:35:25 +0000 hourly 1 http://wordpress.com/ Comment on Math Challenge: All-digits Arithmetic by All-digits Arithmetic: Analysis Part 3 – Digital Substitute https://shawnurban.wordpress.com/2011/06/28/math-challenge-all-digits-arithmetic/#comment-1338 Sun, 22 Sep 2019 23:10:58 +0000 http://shawnurban.wordpress.com/?p=436#comment-1338 […] of and connection between several distinct answers to an All-digits Arithmetic challenge posed in 2011 by Dennis Coble, a fellow tweeter and friend of […]

]]> Comment on All-digits Arithmetic: Analysis Part 2 by All-digits Arithmetic: Analysis Part 3 – Digital Substitute https://shawnurban.wordpress.com/2019/09/15/all-digits-arithmetic-analysis-part-2/#comment-1337 Sun, 22 Sep 2019 23:10:55 +0000 http://shawnurban.wordpress.com/?p=872#comment-1337 […] the last two posts, we explored the determination of and connection between several distinct answers to an All-digits Arithmetic challenge posed in 2011 by Dennis Coble, a […]

]]> Comment on All-digits Arithmetic: Analysis Part 1 by All-digits Arithmetic: Analysis Part 3 – Digital Substitute https://shawnurban.wordpress.com/2019/08/30/all-digits-arithmetic-analysis-part-1/#comment-1336 Sun, 22 Sep 2019 23:10:52 +0000 http://shawnurban.wordpress.com/?p=854#comment-1336 […] the last two posts, we explored the determination of and connection between several distinct answers to an All-digits Arithmetic challenge posed in 2011 […]

]]> Comment on Math Challenge: All-digits Arithmetic by All-digits Arithmetic: Analysis Part 2 – Digital Substitute https://shawnurban.wordpress.com/2011/06/28/math-challenge-all-digits-arithmetic/#comment-1334 Sun, 15 Sep 2019 19:01:41 +0000 http://shawnurban.wordpress.com/?p=436#comment-1334 […] challenge, which I dubbed All-digits Arithmetic, […]

]]> Comment on All-digits Arithmetic: Analysis Part 1 by All-digits Arithmetic: Analysis Part 2 – Digital Substitute https://shawnurban.wordpress.com/2019/08/30/all-digits-arithmetic-analysis-part-1/#comment-1333 Sun, 15 Sep 2019 19:01:38 +0000 http://shawnurban.wordpress.com/?p=854#comment-1333 […] post we walked through a scheme to solve a math challenge posed by Dennis Coble, a fellow tweeter and friend of […]

]]> Comment on All-digits Arithmetic: Analysis Part 1 by shawnurban https://shawnurban.wordpress.com/2019/08/30/all-digits-arithmetic-analysis-part-1/#comment-1327 Sat, 31 Aug 2019 22:07:58 +0000 http://shawnurban.wordpress.com/?p=854#comment-1327 In the fourth summary item (brute analysis of the blown-apart addition table), I did not show any work illustrating how I reduced the number of possible answers from 22 680 to 192.

Essentially I found all digital sums possible for three-digit numbers with digits 1 through 9. These sums range from 3 (minimum free digit) + 4 (minimum borrowing digit) + 1 (minimum lending digit) = 8 to 9 (maximum free digit) + 9 (maximum borrowing digit) + 7 (maximum lending digit) = 25.

I then found all permutations of three digits, from the digits 1 through 9, that add to each of these digital sums. This produced 294 possible totals.

Finally I removed those totals that repeated digits. This gave me the 192 possible totals stated in the fourth summary item.

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