Pick a number

what if i got -15? what letter is that? i started out with 5
If you start out with 5 then you get 4...

You always get 4.
I mean, this test is hardly surprising. We all know that there is only one well known country starting with "D", and one animal that particularly stands out starting with "E". The test is also flawed, as shown by the animal "Eel", where there is no fourth letter.
 
Here's one that my friend thought of.

1. Pick a number between 0 and 36.
2. Add up the digits of your number.
3. Add 8 to your number.
4. Multiply your number by 7.
5. Take the last digit of your number, multiply it by 2, and subtract it from the rest of your number. (121 --> 12 – 2 = 10 or 68 --> 6 – 16 = -10)
6. Square your new number.
7. If your number is less than 25, add 8 to it. If your number is 25 or greater, subtract 41 from it.
8. Find the corresponding letter of the alphabet. (1-->A, 2-->B, etc.)
9. Choose a state whose name begins with that letter.
10. Take the last letter of its capital and choose a state whose name begins with that letter.
11. Take the last letter of the new state's capital and convert it back into a number.
12. Take the square root of the number.
 
Before reading any other posts:

I actually did this algebraically because I wanted to see if I could spot whatever the "trick" is.

My number from 1-10 was u.
1) u
2) (u-5)
3) 3*(u-5)
4) 9*(u-5)^2
5) summing the digits will be a multiple of 9, since this number is clearly divisible by 9, and summing the digits is a way to tell divisibility by 9. I tested the different choices for u at this point and discovered they all sum to 9 at this step except for choosing 5. Choosing 5 gives zero at this step.
6) We will subtract 4 from 9 giving 5 at this step. Had you chosen 5 from the start you will have the answer zero here, but that means you add 5. No matter what the original choice of number was you have the number 5 at this step.
7) 5*2=10 all choices of original numbers give 10 at this step.
8) 10-6=4 all choices of original numbers give 4 at this step.
9) 4->D
10) Denmark (I chose Denmark, but some more choices are: Dominican Republic, Djibouti, Dominica)
11) Elephant (I chose Elephant, but of course there are many other, eel, emu, eft, eagle, earthworm, etc.)
12) Pink (I chose pink but you could do purple, peach, etc.
 
What if I want to spell Denmark how the people from there spell it? (Danmark)
The spelling doesn't depend on where the speaker is from, but on what language he's using. It's Danmark is Danish and Denmark is English, just like Suomi vs. Finland.

And this trick obviously isn't meant to work in other languages than English.
 
Here's one that my friend thought of.

1. Pick a number between 0 and 36.

Again, I want to know your trick here. My number from 0-36 is u.

1) u
2) This determines divisibility by 3. Also, taking this answer (mod 3) will tell me the remainder when dividing my original number by 3. The smallest answer I could have here is 0 and the largest is 11.
3) My answer is in the range of 8-19 at this point.
4) multiplying by 7 gives me the possibility of having 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133 at this step.
5) This is a divisibility test for the number 7. The result of doing this will give me a multiple of 7 at the end of this step, since my number is clearly already divisible by 7. Possible answers at the end of this step are: -7, 0, 7
6) Possible answers at the end of this step are 0, 49
7) I end up with 8 at the end of this step regardless of my original choice of number.
8) 8->H and all choices give H.
9) Hawaii is the only state that starts with H. Everyone has picked this by this step.
10) Honolulu -> u -> Utah (it's the only "U" state).
11) Salt Lake City -> Y -> 25
12) 5

I have to say I like how you use a divisibility test for the number 7 in your trick after multiplying by 7. I figure most people wouldn't know that trick and would not pick up on that.

Chris
 
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