January 10th, 2019, 12:25 PM  #1 
Newbie Joined: Jan 2019 From: Arrakis Posts: 7 Thanks: 0  Thinker Brainteaser
Attached is a picture of the Brainteaser. Instructions: Find how many ways you can spell the word Thinker from left to right. Have Fun,  Diak42 
January 10th, 2019, 02:10 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,370 Thanks: 2007 
20

January 11th, 2019, 08:37 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,117 Thanks: 1002 
T to N = R to N 2*(1 + 3 + 6) = 20 ... as per Skip 
January 13th, 2019, 02:42 PM  #4 
Senior Member Joined: Oct 2016 From: Arizona Posts: 193 Thanks: 34 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems.  
January 13th, 2019, 03:17 PM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,117 Thanks: 1002 
Too bad so sad: need chalk/blackboard to demonstrate 
January 13th, 2019, 04:26 PM  #6 
Senior Member Joined: Oct 2016 From: Arizona Posts: 193 Thanks: 34 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems. 
Oh, I see the flaw in my $2\cdot2\cdot2,\cdot2..$ argument. Some of them do not have $2$ choices.
Last edited by skipjack; January 13th, 2019 at 08:02 PM. 
January 13th, 2019, 06:55 PM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,117 Thanks: 1002 
Start from T to N: how many ways? You should get 10. Now you're finished: answer is 20. Why? Because going from N to R requires the same steps. 
January 13th, 2019, 07:00 PM  #8 
Senior Member Joined: Oct 2016 From: Arizona Posts: 193 Thanks: 34 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems.  
January 13th, 2019, 08:27 PM  #9 
Global Moderator Joined: Dec 2006 Posts: 20,370 Thanks: 2007  
January 14th, 2019, 10:50 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,117 Thanks: 1002 
Well, I was doing it this way: Code: t h i n k e r 41 31 51 21 42 61 1 32 52 7 22 43 62 33 53 44 1 21 31 41 51 61 7 1 21 31 42 51 61 7 1 21 31 42 52 61 7 1 21 32 42 51 61 7 1 21 32 42 52 61 7 That's 5; similarly 1st move going SouthEast; so 10 so far. 1st move going NorthEast (both halves): 1 21 31 42 52 62 7 1 21 32 42 52 62 7 1 21 32 43 52 61 7 1 21 32 43 52 62 7 1 21 32 43 53 62 7 That's another 5; similarly 1st move going SouthEast; so 20 total Last edited by Denis; January 14th, 2019 at 10:53 AM. 

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