 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Maxim, Minerva & Kangaroo (Posted on 2017-04-22) The twins Maxim & Minerva independently replaced the letters in the word KANGAROO upon the following rules:
1. Similar letters are replaced by the same digit
2. The resulting 8-digit number must be divisible by 11.
3. Maxim had to choose the maximal qualifying number, Minerva - the minimal.

Comparing their correct answers they've found out that a certain letter in the word KANGAROO was replaced by the same digit in their independent answers.

Specify WHAT letter and explain WHY.

 No Solution Yet Submitted by Ady TZIDON No Rating Comments: ( Back to comment list | You must be logged in to post comments.) Solution | Comment 2 of 4 | I'll assume the basics: no leading zeros and each letter represents a distinct base 10 digit.

For KANGAROO to be a multiple of 11, the difference (K+N+A+O)-(A+G+R+O) must also be a multiple of 11.  This difference simplifies to K+N-(G+R) = 0 mod 11.

Let Minerva's first three digits be the absolute minimum with the assumptions previously mentioned.  Then KAN=102.  This implies 3-(G+R) = 0 mod 11 with G and R limited to {3,4,5,6,7,8,9}.  The smallest G can be in this equation, given the set of digits available, is G=5, which makes R=9.  Then Minerva has KANGAROO=10250933.

Similarily, Maxim's first three digits are KAN=987.  This implies 16-(G+R) = 0 mod 11 with G and R limited to {0,1,2,3,4,5,6}.  Then the largest G is 5 with R=0.  Then Maxim has KANGAROO=98758066.

Then comparing the numbers is simple:
`KANGAROO1025093398758066`
The letter/digit they have in common is G=5.

 Posted by Brian Smith on 2017-04-22 12:59:24 Please log in:

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