BrainDen.com - Brain Teasers # Pickett

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## Posts posted by Pickett

1. ### multiply 2 palindrome alphametric to be a pandigital number

Spoiler

Technically two solutions (although, they are the "same" solution since ABCBA * CBABC == CBABC * ABCBA):

A=1, B=8, C=9 or A=9, B=8, C=1
18981 x 98189 = 1863725409

2. ### Songs

Spoiler

Speed of Light

Empire of the clouds

The red and the black

Infinite dreams

3. ### 4x4 Table, Difference more than 2

Hmm...trying to figure out where I've gone wrong...

Spoiler

I've found 1024 solutions that satisfy the FIRST rule...but none of those satisfy the second. Still working on it, though...

4. ### 3 x 3 table with constrains

1 hour ago, jasen said:

Reflection works vertically

Ah, I missed a few of the diagonals (I accounted for the center square but not all):

Spoiler

2 unique solutions, 1 reflection per solution (across the X-Axis)

A=1, B=5, C=7, D=8, E=9, F=2, G=3, H=6, I=4       (G+H+I) = (A+B+C) =13
A=3, B=6, C=4, D=8, E=9, F=2, G=1, H=5, I=7       (G+H+I) = (A+B+C) =13

A=7, B=4, C=6, D=2, E=1, F=8, G=9, H=5, I=3       (G+H+I) = (A+B+C) =17
A=9, B=5, C=3, D=2, E=1, F=8, G=7, H=4, I=6       (G+H+I) = (A+B+C) =17

5. ### 3 x 3 table with constrains

Spoiler

So reflections/rotations get a little strange with this because of the fact that you have stated that the middle-left and middle-middle squares can be a difference of 1. This means if you have a solution that works...and then reflect it across the Y-axis, there's a possibility that that reflected solution is not a valid solution anymore. Here's an example of this:

This solution works with the original configuration:

A=1, B=5, C=7, D=8, E=9, F=2, G=3, H=6, I=4       (G+H+I) = (A+B+C) =13

If I reflect that across the Y-axis...you get this (which is no longer valid because E/F have a difference one 1):

A=7, B=5, C=1, D=2, E=9, F=8, G=4, H=6, I=3       (G+H+I) = (A+B+C) =13

With that being said, I could spend the time figuring out which ones are the true reflections/rotations/duplicates (some are easy to figure out) and which ones aren't...but here's all 24 of the possible solutions to the above:

A=1, B=5, C=7, D=8, E=9, F=2, G=3, H=6, I=4       (G+H+I) = (A+B+C) =13
A=1, B=7, C=3, D=8, E=9, F=6, G=5, H=2, I=4       (G+H+I) = (A+B+C) =11
A=1, B=7, C=5, D=8, E=9, F=2, G=3, H=6, I=4       (G+H+I) = (A+B+C) =13
A=3, B=6, C=4, D=8, E=9, F=2, G=1, H=5, I=7       (G+H+I) = (A+B+C) =13
A=3, B=6, C=4, D=8, E=9, F=2, G=1, H=7, I=5       (G+H+I) = (A+B+C) =13
A=3, B=6, C=4, D=8, E=9, F=2, G=5, H=1, I=7       (G+H+I) = (A+B+C) =13
A=3, B=7, C=1, D=8, E=9, F=6, G=5, H=2, I=4       (G+H+I) = (A+B+C) =11
A=3, B=7, C=2, D=8, E=9, F=4, G=5, H=1, I=6       (G+H+I) = (A+B+C) =12
A=5, B=1, C=6, D=8, E=9, F=4, G=3, H=7, I=2       (G+H+I) = (A+B+C) =12
A=5, B=1, C=7, D=8, E=9, F=2, G=3, H=6, I=4       (G+H+I) = (A+B+C) =13
A=5, B=2, C=4, D=8, E=9, F=6, G=1, H=7, I=3       (G+H+I) = (A+B+C) =11
A=5, B=2, C=4, D=8, E=9, F=6, G=3, H=7, I=1       (G+H+I) = (A+B+C) =11
A=5, B=8, C=6, D=2, E=1, F=4, G=7, H=3, I=9       (G+H+I) = (A+B+C) =19
A=5, B=8, C=6, D=2, E=1, F=4, G=9, H=3, I=7       (G+H+I) = (A+B+C) =19
A=5, B=9, C=3, D=2, E=1, F=8, G=7, H=4, I=6       (G+H+I) = (A+B+C) =17
A=5, B=9, C=4, D=2, E=1, F=6, G=7, H=3, I=8       (G+H+I) = (A+B+C) =18
A=7, B=3, C=8, D=2, E=1, F=6, G=5, H=9, I=4       (G+H+I) = (A+B+C) =18
A=7, B=3, C=9, D=2, E=1, F=4, G=5, H=8, I=6       (G+H+I) = (A+B+C) =19
A=7, B=4, C=6, D=2, E=1, F=8, G=5, H=9, I=3       (G+H+I) = (A+B+C) =17
A=7, B=4, C=6, D=2, E=1, F=8, G=9, H=3, I=5       (G+H+I) = (A+B+C) =17
A=7, B=4, C=6, D=2, E=1, F=8, G=9, H=5, I=3       (G+H+I) = (A+B+C) =17
A=9, B=3, C=5, D=2, E=1, F=8, G=7, H=4, I=6       (G+H+I) = (A+B+C) =17
A=9, B=3, C=7, D=2, E=1, F=4, G=5, H=8, I=6       (G+H+I) = (A+B+C) =19
A=9, B=5, C=3, D=2, E=1, F=8, G=7, H=4, I=6       (G+H+I) = (A+B+C) =17

6. ### Magic weird star

Spoiler

Not accounting for rotations, there are 48 solutions to this problem.

If you account for the fact that this can be rotated 6 times, I see 8 unique solutions.

Below are the 8 unique solutions (with each of the 5 other equal rotations shown)...

Solution 1:    A=1, B=2, C=9, D=11, E=6, F=10, G=14, H=4, I=8, J=3, K=5, L=12, M=13
A=13, B=12, C=5, D=3, E=8, F=4, G=14, H=10, I=6, J=11, K=9, L=2, M=1
A=2, B=8, C=10, D=9, E=1, F=3, G=14, H=11, I=13, J=5, K=4, L=6, M=12
A=12, B=6, C=4, D=5, E=13, F=11, G=14, H=3, I=1, J=9, K=10, L=8, M=2
A=8, B=13, C=3, D=10, E=2, F=5, G=14, H=9, I=12, J=4, K=11, L=1, M=6
A=6, B=1, C=11, D=4, E=12, F=9, G=14, H=5, I=2, J=10, K=3, L=13, M=8

Solution 2:   A=1, B=3, C=8, D=12, E=5, F=10, G=14, H=4, I=9, J=2, K=6, L=11, M=13
A=13, B=11, C=6, D=2, E=9, F=4, G=14, H=10, I=5, J=12, K=8, L=3, M=1
A=3, B=9, C=10, D=8, E=1, F=2, G=14, H=12, I=13, J=6, K=4, L=5, M=11
A=11, B=5, C=4, D=6, E=13, F=12, G=14, H=2, I=1, J=8, K=10, L=9, M=3
A=9, B=13, C=2, D=10, E=3, F=6, G=14, H=8, I=11, J=4, K=12, L=1, M=5
A=5, B=1, C=12, D=4, E=11, F=8, G=14, H=6, I=3, J=10, K=2, L=13, M=9

Solution 3:    A=1, B=5, C=12, D=8, E=3, F=4, G=14, H=10, I=11, J=6, K=2, L=9, M=13
A=13, B=9, C=2, D=6, E=11, F=10, G=14, H=4, I=3, J=8, K=12, L=5, M=1
A=5, B=11, C=4, D=12, E=1, F=6, G=14, H=8, I=13, J=2, K=10, L=3, M=9
A=9, B=3, C=10, D=2, E=13, F=8, G=14, H=6, I=1, J=12, K=4, L=11, M=5
A=11, B=13, C=6, D=4, E=5, F=2, G=14, H=12, I=9, J=10, K=8, L=1, M=3
A=3, B=1, C=8, D=10, E=9, F=12, G=14, H=2, I=5, J=4, K=6, L=13, M=11

Solution 4:    A=1, B=6, C=11, D=9, E=2, F=4, G=14, H=10, I=12, J=5, K=3, L=8, M=13
A=13, B=8, C=3, D=5, E=12, F=10, G=14, H=4, I=2, J=9, K=11, L=6, M=1
A=6, B=12, C=4, D=11, E=1, F=5, G=14, H=9, I=13, J=3, K=10, L=2, M=8
A=8, B=2, C=10, D=3, E=13, F=9, G=14, H=5, I=1, J=11, K=4, L=12, M=6
A=12, B=13, C=5, D=4, E=6, F=3, G=14, H=11, I=8, J=10, K=9, L=1, M=2
A=2, B=1, C=9, D=10, E=8, F=11, G=14, H=3, I=6, J=4, K=5, L=13, M=12

Solution 5:    A=2, B=4, C=6, D=13, E=5, F=11, G=14, H=3, I=9, J=1, K=8, L=10, M=12
A=12, B=10, C=8, D=1, E=9, F=3, G=14, H=11, I=5, J=13, K=6, L=4, M=2
A=4, B=9, C=11, D=6, E=2, F=1, G=14, H=13, I=12, J=8, K=3, L=5, M=10
A=10, B=5, C=3, D=8, E=12, F=13, G=14, H=1, I=2, J=6, K=11, L=9, M=4
A=9, B=12, C=1, D=11, E=4, F=8, G=14, H=6, I=10, J=3, K=13, L=2, M=5
A=5, B=2, C=13, D=3, E=10, F=6, G=14, H=8, I=4, J=11, K=1, L=12, M=9

Solution 6:    A=2, B=5, C=13, D=6, E=4, F=3, G=14, H=11, I=10, J=8, K=1, L=9, M=12
A=12, B=9, C=1, D=8, E=10, F=11, G=14, H=3, I=4, J=6, K=13, L=5, M=2
A=5, B=10, C=3, D=13, E=2, F=8, G=14, H=6, I=12, J=1, K=11, L=4, M=9
A=9, B=4, C=11, D=1, E=12, F=6, G=14, H=8, I=2, J=13, K=3, L=10, M=5
A=10, B=12, C=8, D=3, E=5, F=1, G=14, H=13, I=9, J=11, K=6, L=2, M=4
A=4, B=2, C=6, D=11, E=9, F=13, G=14, H=1, I=5, J=3, K=8, L=12, M=10

Solution 7:    A=3, B=4, C=5, D=13, E=6, F=12, G=14, H=2, I=8, J=1, K=9, L=10, M=11
A=11, B=10, C=9, D=1, E=8, F=2, G=14, H=12, I=6, J=13, K=5, L=4, M=3
A=4, B=8, C=12, D=5, E=3, F=1, G=14, H=13, I=11, J=9, K=2, L=6, M=10
A=10, B=6, C=2, D=9, E=11, F=13, G=14, H=1, I=3, J=5, K=12, L=8, M=4
A=8, B=11, C=1, D=12, E=4, F=9, G=14, H=5, I=10, J=2, K=13, L=3, M=6
A=6, B=3, C=13, D=2, E=10, F=5, G=14, H=9, I=4, J=12, K=1, L=11, M=8

Solution 8:    A=3, B=6, C=13, D=5, E=4, F=2, G=14, H=12, I=10, J=9, K=1, L=8, M=11
A=11, B=8, C=1, D=9, E=10, F=12, G=14, H=2, I=4, J=5, K=13, L=6, M=3
A=6, B=10, C=2, D=13, E=3, F=9, G=14, H=5, I=11, J=1, K=12, L=4, M=8
A=8, B=4, C=12, D=1, E=11, F=5, G=14, H=9, I=3, J=13, K=2, L=10, M=6
A=10, B=11, C=9, D=2, E=6, F=1, G=14, H=13, I=8, J=12, K=5, L=3, M=4
A=4, B=3, C=5, D=12, E=8, F=13, G=14, H=1, I=6, J=2, K=9, L=11, M=10

7. ### Equal product of dots in Hexagon

Spoiler

For what it's worth, if rotation and reflection are NOT considered one solution, then there are 196 answers...

Also, interestingly, all solutions have a product of 27,000.

Here's one configuration that works:

a=2, b=6, c=3, d=15, e=5, f=10, g=75, h=50, i=20, j=12, k=18, l=45

8. ### Replace Letters.

Spoiler

For second question:

ABCDEFGHI     ABCDEFGHI
182975346 and 271985346

18 * 297 = 27 * 198 = 5346

27 * 198 = 18 * 297 = 5346

9. ### To die or not to die ...

I'd say nothing...as being "HUNG" from a gallows pole implies there is no intent to kill...

If they were actually trying to kill the criminal he would be "HANGED" from the gallows pole.

This has been a lesson from your friendly neighborhood grammar nazi...  10. ### Dash?

The name of the game is "Nim" for what it's worth...

Full strategies and math behind it can be found on the Wikipedia page:

https://en.wikipedia.org/wiki/Nim

11. ### Who is taller, A or B?

99% of the time, B will be taller.

12. ### A simple multiple-choice test

Explanation:

If 1 = A...that doesn't work, because Question one is not answer B.
If 1 = B...that doesn't work, because Question one is B...
If 1 = D, then 2 = B, which means 4 = A. If that is true, then 3 = D and 5 = D...but that can't be true, since question 1's answer is not A. Therefore 1 != D.

So 1 = C. This means 3 = B.
If 2 = A...Then 4 = D, but that can't be, since 4 is D.
If 2 = B...Then 4 = A, but that can't be, since there aren't 3 answers left to be D
If 2 = C...Then 4 = B, but that can't be true, because there aren't 2 answers left to be D
So 2 = D, This means 4 = C
If 5 = D, that doesn't work, because now answer 4 is wrong
If 5 = A, that doesn't work because 3 = B
If 5 = C, that doesn't work, because there aren't 3 answers that are B
So 5 = B

Final answer: 1=C, 2=D, 3=B, 4=C, 5=B

13. ### Marathon (mini) puzzles (trapped in a dungeon)

Ok...I'll bite

14. ### 11 Letters

Yes, similar to the classic riddle: "Rearrange the letters of "NEW DOOR" to create one word."

The answer in that case is "ONE WORD"...

So the answer to this puzzle is "ONLY ONE WORD"

15. ### Bees

The attachment you included is broken...so I don't know if my assumption on the description of the problem is correct, but assuming I read it correctly...the answer is:

1320 cm3

V = (3*sqrt(3)/2)a2h

We know from the description that h (height) = 11cm

We can use the other clues to determine a (length of a base edge) = sqrt((320/3) * sqrt(3)) / 2

So simply plugging it in, we get

V = (3*sqrt(3)/2)(320*sqrt(3)/12)(11)

V = (2880/24)(11)

V = 1320cm3

16. ### School

20 Snakes (22 heads, 0 legs)

19 Birds (20 heads, 38 legs)

23 Turtles (23 heads, 91 legs)

13 Insects (13 heads, 76 legs)

22 Spiders (22 heads, 175 legs)

17. ### brain teaser sent by a friend that I can't solve

not much of a brain teaser...just giving you their email address...

18. ### Maths Teaser 2

Might not be minimum...

But you could deliver the message to Mr. Harvey in AT WORST 50 minutes...or 25 calls.

Start by calling the 25th person on the list....if their name is earlier (alphabetically) than Mr. Harvey, then call the 49th person on the list (24 further)...if if that person is still earlier than Mr. Harvey, call the 72nd person on the list (23 further)...etc...etc...until you get a person that is later (alphabetically) than him. Once you find someone "later", you simply start calling one at a time between the two...

You could actually then do a divide and conquer approach once you have it narrowed down, which in the long term would make the search faster...but for a SINGLE instance like the OP...to GUARANTEE the message is delivered, it doesn't matter if you do one at a time or divide and conquer, it would still be at worst 25 calls.

19. ### Folding a paper into a sphere

I can take any shape/size paper and crumple it into a ball...VOILA! a single sheet of paper "folded" into a sphere!

But seriously...I think we're starting to get into Map projections here...

There's probably a "more correct" answer, the but Goode Homolosine projection is pretty darn close...

20. ### Base 10 and base 3 equivalents

A couple more...

Just for completeness: -15, -14, 0, 14, 15

21. ### Image puzzles

In the second image

It's not much, and probably not down the right track...but the boxes seem to contain Morse Code for OMOM

22. ### Anagrams for Fun - I: Defintions?

Finally...

#9 The public art galleries (that one was really difficult...once I saw "galleries" in there, it started making sense)

While I have certainly enjoyed these, any reason they're in the math puzzles section, not the words puzzles section?

23. ### Anagrams for Fun - I: Defintions?

#6: Snooze Alarms

#9 ????

24. ### Anagrams for Fun - II: Quotations

"To be or not to be: that is the question, whether tis nobler in the mind to suffer the slings and arrows of outrageous fortune."

"That's one small step for a man, one giant leap for mankind" -Neil Armstrong

Ok, yeah, those are pertty good...

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