Difference between revisions of "AoPS Wiki talk:Problem of the Day/June 6, 2011"
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{{:AoPSWiki:Problem of the Day/June 6, 2011}} | {{:AoPSWiki:Problem of the Day/June 6, 2011}} | ||
==Solution== | ==Solution== | ||
− | { | + | |
+ | |||
+ | Just rewrite the numbers over and over and get rid of every 9th: | ||
+ | |||
+ | 1 2 3 4 5 6 7 8 9 Remove the 9 | ||
+ | |||
+ | 10 11 12 1 2 3 4 5 6 Remove the 6 | ||
+ | |||
+ | 7 8 10 11 12 1 2 3 4 Remove the 4 | ||
+ | |||
+ | 5 7 8 10 11 12 1 2 3 Remove the 3 | ||
+ | |||
+ | 5 7 8 10 11 12 1 2 5 Remove the 5 | ||
+ | |||
+ | 7 8 10 11 12 1 2 7 8 Remove the 8 | ||
+ | |||
+ | 10 11 12 1 2 7 10 11 12 Remove the 12 | ||
+ | |||
+ | 10 11 1 2 7 10 11 1 2 Remove the 2 | ||
+ | |||
+ | 7 10 11 1 7 10 11 1 7 Remove the 7 | ||
+ | |||
+ | 10 11 1 10 11 1 10 11 1 Remove the 1 | ||
+ | |||
+ | 10 11 10 11 10 11 10 11 10 Remove the 10 | ||
+ | |||
+ | The last number to be destroyed is <math>\boxed{11}</math>. |
Latest revision as of 22:55, 10 June 2011
Problem
AoPSWiki:Problem of the Day/June 6, 2011
Solution
Just rewrite the numbers over and over and get rid of every 9th:
1 2 3 4 5 6 7 8 9 Remove the 9
10 11 12 1 2 3 4 5 6 Remove the 6
7 8 10 11 12 1 2 3 4 Remove the 4
5 7 8 10 11 12 1 2 3 Remove the 3
5 7 8 10 11 12 1 2 5 Remove the 5
7 8 10 11 12 1 2 7 8 Remove the 8
10 11 12 1 2 7 10 11 12 Remove the 12
10 11 1 2 7 10 11 1 2 Remove the 2
7 10 11 1 7 10 11 1 7 Remove the 7
10 11 1 10 11 1 10 11 1 Remove the 1
10 11 10 11 10 11 10 11 10 Remove the 10
The last number to be destroyed is .