Puzzles

[robb]

@ByteInBits, A nice ordered puzzle requiring thought!

[ByteInBits]

Thanks for the comment @robb

[Kingswinford-Warriors-Alumni]

Cheers @robb! (P.S. Feel free to post something along the lines of MD5(Name + Answer) in the forums if you wish to prove your problem-solving skills to the Cipher Challenge community!)

[ByteInBits]

@Kingswinford-Warriors-Alumni – Ref. Puzzle 2

The grids are not displaying correctly
With 3 full stops together they mess up in the forum
Compare, here are 3 full stops …
and 3 with spaces between them . . .

========================= Your grids redone (they should show ok now)
But please check and confirm they are correct.

Grid W:
. ? . . . . .
? ? ? . . . .
. ? ? ? ? . .
. . ? ? ? . .
. . . ? ? ? ?
. . . ? . . .

Grid X:
? ? ?
? ? ?
? ? ?
. ? .

Grid Y:
? ? ? ? ? . .
? . . . ? ? ?
? ? ? ? ? . .
? ? ? ? . . .
. ? ? ? . . .
. . ? . . . .

Grid Z:
? ? ? . .
? ? ? ? .
? ? ? ? .
. ? ? ? ?
. . . ? .

=========================================
Helpfully: I think your grids would be better presented as I give here.
With x representing a blacked out square, what do you think?

Grid W:
|x|_|x|x|x|x|x|
|_|_|_|x|x|x|x|
|x|_|_|_|_|x|x|
|x|x|_|_|_|x|x|
|x|x|x|_|_|_|_|
|x|x|x|_|x|x|x|

Grid X:
|_|_|_|
|_|_|_|
|_|_|_|
|x|_|x|

Grid Y:
|_|_|_|_|_|x|x|
|_|x|x|x|_|_|_|
|_|_|_|_|_|x|x|
|_|_|_|_|x|x|x|
|x|_|_|_|x|x|x|
|x|x|_|x|x|x|x|

Grid Z:
|_|_|_|x|x|
|_|_|_|_|x|
|_|_|_|_|x|
|x|_|_|_|_|
|x|x|x|_|x|

I have not solved all the puzzles and doubt that I will!

[ByteInBits]

@Kingswinford-Warriors-Alumni
Sorry I forgot to say when they are copy and pasted into Notepad or the like is when they do not display correctly.

[Kingswinford-Warriors-Alumni]

Again, I haven’t had time to try this for myself, but it looks fun! Harry

Since I seem to be in the mood for merging puzzles of the same type at the moment, here is another puzzle where you have to solve several things at once! This one comes with a mild warning:

WARNING: Hard! (probably)

Everything OK? Good. Have fun! [This introduction is not a puzzle.]

Puzzle Hunt, Puzzle 3: Broken Bits (4,4,8)
MD5: 5e32133d076828c733c6baeb283e63cf

[PUZZLE]

A good lesson for you folks out there – never leave two unsolved sudokus together unattended. You never know what will happen if they get mixed up…

(Hint: To get the answer, you might want a slanted look at things!)

Grids:

????..KD
????….
????.D.U
????O.G.
????????
????????
U..O????
..E.????

????.VUR
????L…
????????
????????
.E.O????
U…????
.RO.????
..NV????

[N.B. Both grids are standard 8×8 sudoku grids, consisting of eight blocks that are all 4 columns wide by 2 rows high. ‘.’ represents a square that is known to be blank at the start of the puzzle, and ‘?’ represents an unknown square that may or may not be blank at the start of the puzzle. This note is not a puzzle.]

Missing blocks:

DE.L ..VO .U.N O.UK .CL.
.GO. ENL. ..EL D… K..E

..DG …U .K.. .L.. ….
K..O OY.. LU.. OR.. ….

[N.B. The above list consists of ten blocks (arranged in two rows) that are all 4 columns wide by 2 rows high. If you cannot see the blocks clearly, try using a monospaced font (e.g. Courier New). ‘.’ represents a square that is known to be blank at the start of the puzzle. This note is not a puzzle.]

[Kingswinford-Warriors-Alumni]

@ByteInBits, #97819

Thanks for alerting me! Your corrected grids are correct (and I like the second idea you gave!), and I will try to format the grids slightly differently in future.

Here are some corrected grids for Puzzle 3, with full stops replaced by commas:

Grids:

????,,KD
????,,,,
????,D,U
????O,G,
????????
????????
U,,O????
,,E,????

????,VUR
????L,,,
????????
????????
,E,O????
U,,,????
,RO,????
,,NV????

Missing blocks:

DE,L ,,VO ,U,N O,UK ,CL,
,GO, ENL, ,,EL D,,, K,,E

,,DG ,,,U ,K,, ,L,, ,,,,
K,,O OY,, LU,, OR,, ,,,,

[_madness_]

Thanks Madness, this, as usual, is really helpful! Harry

Hi, everyone. Madness here. I see that there is some trouble with grids looking poorly on the forum. Here are two things that you can do:
1. Use the HTML “pre” tag around the stuff that you want to appear in a monospaced font. So begin with “<” + “p” + “r” + “e” + “>” and end with “<” + “/” + “p” + “r” + “e” + “>”. The tag is an abbreviation for “preformatted”.
2. If you see “CODE” in a bar above the editor box into which you type your post, click it before adding the grid stuff, and click “/CODE” after. This will insert some single quotation marks that tell the forum to use monospace fonts.

Here are the two in action:

This one uses the "pre" tag."
A B C D E
F G H I J
K L M N O
P Q R S T
U V W X Y
and Z is pronounced "zee".

This one uses the CODE button.
A B C D E
F G H I J
K L M N O
P Q R S T
U V W X Y
and no one uses Z anyway.

[ByteInBits]

@_madness_
Ha Ha it’s pronounced “zee” in USA it is sounds like “said” in UK
I once saw an USA man on YouTube saying “zee X spectrum” (80’s UK computer) it sounds so wrong to us (“said X spectrum”)
but kindly we do say “zee zee tops” USA pop group and not “said said tops”. 😉

[Kingswinford-Warriors-Alumni]

@_madness_ (#97849)

So THAT’s what the CODE tag does! (Thanks for the help!) [P.S. Harry, could you reveal what all of the other tags are? Stuff like ‘B’ and ‘I’ are easy enough to understand, but I have no idea what things like ‘OL’ or ‘LI’ are meant to mean…]

1. OL = ordered (numbered) list
2. LI = list item

• UL = unordered (bulleted) list
• Harry

Hopefully this will be third time lucky with my grids for Puzzle 3:

Grids:

????..KD
????....
????.D.U
????O.G.
????????
????????
U..O????
..E.????

????.VUR
????L...
????????
????????
.E.O????
U...????
.RO.????
..NV????

Missing blocks:

DE.L ..VO .U.N O.UK .CL.
.GO. ENL. ..EL D... K..E

..DG ...U .K.. .L.. ....
K..O OY.. LU.. OR.. ....

[robb]

@Kingswinford, everyone will need to think hard particularly on the second grid. My choice on the first was fortuitous and gave me a good starting base grid to solve it! 😉

[ByteInBits]

When in Rome
============

When I was learning Latin my buddy showed me the following,
A slab of excavated stone from Rome, with a metal spike driven into one end
and a large metal ring attached to that, on one side of the slab was writing
as shown here. . .

 _______
|\      \
| \______\
| |      |
| | TOTI |
| |  E   |
| | HORS |
| | ESTO |
 \|______|

He asked me what do I think the Romans used it for.
Well now what do YOU think it was used for?

[USB-C_is_supreme]

Hi fellow puzzle lovers!

I have a maths puzzle that is simple but brilliant, and the solution is quite fun. Here it is:

Katie pretends she has a pack of cards numbered 1 to 10,000. She removes every card that has a square number writen on it, leaving a certain amount of cards, N, left in the deck. She then rubs out all the numbers on the remaining cards and renumbers them 1 to N. This step is repeated with N getting smaller after every step.

How many steps are needed until there is only 1 card remaining?

Hope you had fun solving this!

-USB-C

[_madness_]

@USB-C, since Katie is only pretending, there will never be any cards.

[upsidedown]

Nice puzzle USB-C, I did indeed have fun solving it!

My solution:

Note that 10000 = 100 squared. At any step, the root of the largest square number not more than N is the integer part of the square root of N. Since we remove this square number, and any squares less than it, this square root equals the total number of cards removed.

Suppose we have N = (n + 1)^2 for integer n >= 1.

1. First step: N = n^2 + n + (n + 1); and int(sqrt(N)) = n + 1. So N – int(sqrt(N)) = n^2 + n = n(n + 1).
2. Second step: Now N = n(n + 1). So int(sqrt(N)) = n. Therefore N – int(sqrt(N)) = n^2 + n – n = n^2.

So when N is (n + 1)^2 for integer n >= 1, we can always take two steps and will end up with n^2 as the new N.

We begin with n + 1 = 100, and end with n + 1 = 2 (because after taking two steps we have n^2 = 1^2 = 1). Therefore there are a total of 99 values of n (n = 99, …, n = 1). So the number of steps is 99*2 = 198.

[Author]

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