My Math Forum Thinker Brainteaser

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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
Attached Images
 Thinker Brainteaser.jpg (12.1 KB, 13 views)

 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 Thanks from ProofOfALifetime
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.
Quote:
 Originally Posted by Denis T to N = R to N 2*(1 + 3 + 6) = 20 ... as per Skip
Apparently, I'm not good at this because I don't even see how you got that. I mean the 1+3+6 part

 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 Thanks from ProofOfALifetime
 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. Thanks from ProofOfALifetime
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.
Quote:
 Originally Posted by Denis 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.
Okay cool I guess I was over thinking

January 13th, 2019, 08:27 PM   #9
Global Moderator

Joined: Dec 2006

Posts: 20,370
Thanks: 2007

Quote:
 Originally Posted by Denis Start from T to N: how many ways? You should get 10.
From T to N, one gets 1 + 3 + 3 + 1 = 8.
Extending that to K gives 4 + 6 + 4 = 14.
Extending that to E gives $\!$ 10 + 10 = 20.
Extending that to R also gives 20.

 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 1st move going North-East (top half): 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 South-East; so 10 so far. 1st move going North-East (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 South-East; so 20 total Last edited by Denis; January 14th, 2019 at 10:53 AM.

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