# A small problem

1. May 14, 2005

### Rahmuss

This is a multi-part question. I made it up, so it may not be perfect. I looked through it pretty good before posting it here. If you think something is wrong or have a question, the message me about it. Thanks. This one is for all you smarty-pants out there. There is one spot where you have to make an intuitive jump, the rest can be reasoned out, or be found by using simple math. If it's Ok, please message me the answer before posting in white in case you get part of it correct; but not all of it.

Three scientists claim to be the most intelligent. The head of the most highly coveted scientist position will give up his place to the one deemed to be most intelligent of the three.
To do this, he has setup a test where they will compete against the other two.
Each scientist was blind folded and then a symbol was painted on their foreheads. The color of the symbol can be red or blue and can be either a stone, a leaf or a bird.
When the blindfolds were removed, the head scientist told each of them that they had either a red or a blue symbol on their forehead.
The head scientist then asked them to raise one hand if they saw a red symbol on the head of at least one person. Each of them raised one hand.
After that, the head scientist told them to figure out what color of symbol was on their own foreheads. Time passed and none of the scientists said anything.
Then one scientist stepped forward to give his answer. His answer was correct. What did he say?

If his answer was a color, then x = number of symbols represented by that color.
If his answer was something else, then x = 5.

3x + 2£ - 1æ = 9
5x + 3£ + 2æ = 36
What are £ and æ?

£, æ, 9, 10, a, b
With the sequence above, what are a and b? (Use Base 12 number system to determine your answer.)

Place a "O" in the corresponding number for a and b along with the first grid provided, the rest will be dashes.
This creates a pattern. What number are the slots for the fourth grid using the number grid below?
01 02 03 04
05 06 07 08
09 10 11 12
13 14 15 16

For example... if a = 4 and b = 2, and the initial two positions in 7 and 11 are given, then the first grid will look like this:

- O - O
- - O -
- - O -
- - - -

Grid# 1:
? ? ? ?
? ? O ?
? ? O ?
? ? ? ?

Grid# 2:
O - - O
- O - -
- O - -
- - - -

Grid# 3:
O - - O
- O - -
- O - -
- - - -

Grid# 4:
? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?

Lowest number "O" is #a, the next lowest number "O" is #b, and so on to #c and finally #d.

Clue me in.
Decipher:
15 10 01 02 04 09 09,
T 01 03 09
W 10 09
#d 10 09 #c
03
10 02
#a 03 N #b

Last edited: May 15, 2005
2. May 14, 2005

### BicycleTree

You lost me after æ = 7 and E = 3.5

3. May 14, 2005

### Rahmuss

I changed the second line to this:

3x + 2£ - 1æ = 9
5x + 3£ + 2æ = 36

I'm not sure how I missed that; but there it is. For the characters £ = Alt + 156, æ = Alt 145. Sorry about that.

4. May 17, 2005

### Rahmuss

Is this too hard or two dumb?
I did this hoping to stump some smart people; but I don't think it's really THAT hard.... is it? Or is it just lame?

5. May 17, 2005

### mapper

I believe there is already a riddle just like this but with hats...

6. May 17, 2005

### Rahmuss

Actually, the riddle with the hats is different, and mine also has more parts to it to decipher the final code. Each stage gives you the needed information for the next stage. Except for the last problem you have to make an intuitive leap from a clue given.

7. May 17, 2005

### T@P

this is what i think

first of all since time passed and no one answered any question, this must mean the configuration of red and blue is the 'hardest', i.e. not obvious in one sec.

with that in mind, since each person saw at least one red, at least two people have red marks. WLOG, lets consider this from the perspective of scientist 1. he sees a red mark on someones head. now if he sees only one, then that means he must have a red sign on his head because if he didnt then only two people have red marks and one person doesnt see any red at all (the one with that only red mark) clearly he sees two. now comes the iffy part. *if* someone were to immediately know the answer that would mean that that person only sees one red mark. (same reasoning as above). therefore, since time passed and no one answered the question, everyone sees two red marks and hence his head is red.

oh and sorry about the extra long reply, i was working this out as i typed.
(exclusive look at my thought process :rofl: )

oh and these problems are quite cute. i like them, so dont get discouraged if you dont get a reply fast. i dont live on this board yknow

i got lost after the the sequence, how is
3,6,9,10 a sequence? changing to base twelve doesnt do much... unless you mean the funny number plus letter combo. if thats the case i bow out now, since i dont know it . i think the 10 should be a 0. it would make more sense...

Last edited: May 17, 2005
8. May 18, 2005

### Rahmuss

Great answers. You're right on track. As to your question with part 3, read in white below.

Counting from base 12, it would look like: 1,2,3,4,5,6,7,8,9,a,b,10,11,12,13,14,15,16,17,18,19,1a,1b,20 ... etc... 98,99,9a,9b,a0,a1,a2... a9,aa,ab,b0,b1,b2... etc...

Where a represents the value of 10 (but not the number 11) and b represents the value of 11 (but not the number). So if you read it that way, then 3,6,9,10 is a pretty simple pattern.

Does that help?

9. May 18, 2005

### T@P

oh.. so then
it would be 3 6 9 10 (but ten is like the the first time you finished a cycle of 12...) so in base 10 it would be 3 6 9 12 15 18 where a and b are then 3 and 5...

frankly im a bit lost on the O part.

but its really too bad that the actualy puzzlers ended, the rest is more stuff you see in those like word puzzles books, only there its with crossword type clues.

got anymore puzzles like the first one? ( i really enjoyed that one)

10. May 19, 2005

### Rahmuss

You're right on track here... so the pattern is just like you have listed in base 10, so in base 12 "10" = the value of 12 and then "13" would be the value of 15 and "16" would be the value of 18.

I've included an image here : http://img216.echo.cx/my.php?image=boxpattern5yr.png
This should give you a better picture.
Grid "A" shows how they're numbered, so once you get the next two values in the series from the part right before this one, you plug in a blue sphere right where those number values go.
Grid "B" shows how it would look if the values you got were 2 and 4 (which they're not ).
Grid "C" gives you two of the four spheres. The other two spheres are at the location found by the last two numbers of that series. So that there will be four spheres in there.
Grid "C", "D" and "E" make up a pattern (once you've found Grid "C" it's not too hard).
Grid "F" is the continuation of that pattern which then gives you values to equate to letters for the last puzzle.

If you mean the one with the three scientists, nope. sorry. I'll look and see what I can find though.

Last edited: May 19, 2005