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January 10th, 2019, 12:25 PM   #1
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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
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File Type: jpg Thinker Brainteaser.jpg (12.1 KB, 13 views)
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January 10th, 2019, 02:10 PM   #2
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20
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January 11th, 2019, 08:37 AM   #3
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T to N = R to N

2*(1 + 3 + 6) = 20 ... as per Skip
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January 13th, 2019, 02:42 PM   #4
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Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems.
Quote:
Originally Posted by Denis View Post
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
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January 13th, 2019, 03:17 PM   #5
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Too bad so sad: need chalk/blackboard to demonstrate
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January 13th, 2019, 04:26 PM   #6
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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.
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January 13th, 2019, 06:55 PM   #7
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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.
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January 13th, 2019, 07:00 PM   #8
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Quote:
Originally Posted by Denis View Post
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
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January 13th, 2019, 08:27 PM   #9
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Quote:
Originally Posted by Denis View Post
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.
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January 14th, 2019, 10:50 AM   #10
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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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