Commander

13 hours ago, md65536 said:

1.

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10x10 is the only square possible? Or am I missing something?

2.

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With the cube edges aligned with x y z axes, cut with a normal of (1, 1, 1).

Or in other words, align the cube with 2 opposite corners on a vertical axis, and make a horizontal cut. The cut should go through the midpoint of 2 adjacent edges on each of the cube's faces, separating each face into an area that is 7/8 of the original, and a corner cut off that is the other 1/8.

 

Yes, there is another Square possible.

On the second point you seem to be on the right track. However the exact cut must be spelt out on the 10 Cm edges.

The Brain Teaser here is about cutting a Perfect Cube [let's take the one with 10 Cms edge] into two equal parts and discussing about the CUT FACE or the newly created SURFACE of the Planar Cut.

Obviously for the remnants to be equal and identical the CUT must pass through the CENTRE of the Cube which is a sufficient criteria.

We are not bothered about the multi-cuts and their effects such as producung a perfect tetrahedron and four other equal pieces. 

Now we can see that this single cut can leave a CUT FACE of a Square exactly equal to one face of the Cube. Or can produce a CUT FACE of a Rectangle with one edge and one diagonal as its sides.

What is asked is :

1. What is the largest such Square CUT FACE which can be produced.

2. What is the Cut which will result in a HEXAGONAL CUT FACE leaving two pieces having 7 faces or shapes [one Hexagon and six others]

............................

PS :

This must be quite easy !

This Poll is closed now ! TY all !!

OK TY

Oh OK, TY swansont , Is it possible to move it to another area like lounge 

'Which is the most progressive Human Invention among the following ' What will you pick? https://pollsgo.com/poll?p=ohCWHqd

To be a TRUE SCIENTIST One must be :

100 % in OBSERVATION

100 % Logical in Deductions

100 % Testing the Theories

100 % expect Criticism and Explain

100 % Ready to be Responsible for Conclusions

………………………………..

Why Fight

Like Animals in a Jungle

When you can Mingle & Live

Happily as a Society

Granting each other Right to exist

With Equality and Respect

Any Hero or King

Lives, Enjoys and dies

Some do Good some Evil

Loved or hated by masses

Many forgotten except those

Uplifting whole Society

...................................................................

There was a young Lady from Niger

Who smiled as she rode on a Tiger;

They returned from the ride

With the lady inside,

And the smile on the face of the Tiger.

.......................................................

USA the Most Powerful Nation

Must be lead with due Caution

Preventing Global Disaster

Without Noise and Bluster

By any ABC, Trump or Clinton

...........................................................

Money is like Honey

Which is hoarded by Many

But needed as Life Support

For Societies of all sort

Let us Share it with all

Treating them Equal

I may learn so many 
But be no slave to any
Want to remain rooted
In Truth : be surefooted

...................................................................................

Birds of ATTRACTIVE FEATHERS FLOCK Together

.....................................................................................

WISDOM is like a DAM which

Holds Every Information which reaches it but

ONLY RELEASES the NECESSARY and NEEDED KNOWLEDGE out  

Sensei : only 7722 will make it !

Which is also double of 3861

16 hours ago, Ghideon said:

Ghideon :

Absolutely Right ! Well done !!

 

Yes you are to assume that 

Yes the reply has not been given though the fact is Mr. Johnson needed to ask it ! 

Yes a unique Solution is expected !

There is a four-digit number ABCD, where A, B, C, D each represents a different digit from 1 to 9.

ABCD is divisible by 13,  BCDA is divisible by 11, CDAB is divisible by 9, and DABC is divisible by 7.

Can you find the original number ABCD ?

Some children were playing in the Garden.

Mr. Johnson asked Mrs. Albert if they were all hers.

“No” she replied. “ My children are playing with friends from

3 other Families “.

“Our Family happens to be the largest, The Berry Family have a smaller

Number of Children, The Charles Family have an even smaller number

and  the Dickens have the smallest of all”.

“How many children altogether ?” asked Mr. Johnson.

Mrs. Albert replied , “There are fewer than 18 and the product of the

Numbers in the 4 Families happens to be my House number which you

already know”. Mr. Johnson asked if there was more than one child in the

Dickens Family. Mrs Albert replied.

How many children are there in each family ?

As advised by the Moderator the related Puzzle is posted in a separate topic 

Plz reply to that Puzzle in the new Thread.

I think this puzzle needs to be restated by the proposer again so that any ambiguity is removed !

Also I think the Puzzle is that a,b,c,d are all from digits 1 to 9 [no zero] each unique and you can have a > b> c> d !

The question is to find the smallest 4 digit number which will satisfy this as well as the Conditions stated for Jack, John and James !

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

As an aside please solve this related Puzzle :

Some children were playing in the Garden.

Mr. Johnson asked Mrs. Albert if they were all hers.

“No” she replied. “ My children are playing with friends from

3 other Families “.

“Our Family happens to be the largest, The Berry Family have a smaller

Number of Children, The Charles Family have an even smaller number

and  the Dickens have the smallest of all”.

“How many children altogether ?” asked Mr. Johnson.

Mrs. Albert replied , “There are fewer than 18 and the product of the

Numbers in the 4 Families happens to be my House number which you

already know”. Mr. Johnson asked if there was more than one child in the

Dickens Family. Mrs Albert replied.

How many children are there in each family ?

I thought this was already solved by someone

Yes AjkC is absolutely Right ! Well done 

Yes,

These are the two combinations !

You are very good in programming !

I have so far been able to use Excel for these Puzzles with success !

Hi Sensei,

Yes, a good answer !

I got 3025 and if you can better it it will be interesting !

Is there a Combination for a score more than 3025 ?

A more involved Puzzle will be :

Your Mission is to find the best score for the pattern 

     a  b  c
     d  e  f
     g  h  i     where a to i stand for one of 1 2 3 4 5 6 7 8 9 uniquely !

for example     9  7  5
                        8  4  3
                        6  2  1

The Pattern Score is calculated as :

 =  Rows – Columns + Product of Diagonals – Product of Corners + Product of Ribs – Product of Diamond 
     +  Sum of Corners + Sum of Squares of Diamonds + Cube of the Center Number

Which means in the example pattern the Score is :
= 975+843+621 –986–742–531 + 9*4*1+6*4*5–9*5*1*6 +8*4*3+7*4*2– 8*7*3*2 +9+5+1+6+8^2+7^2+3^2+2^2+4^3
= 93

Find the Pattern for getting the HIGHEST SCORE !

Your Mission is to find the best score for the pattern 

     a  b  c
     d  e  f
     g  h  i     where a to i stand for one of 1 2 3 4 5 6 7 8 9 uniquely !

for example    1  2  3
                        4  5  6
                        7  8  9

The Pattern Score is calculated as :

 =  Rows–Row Products+Columns–Column Products–Product of Diagonals–Product of Corners–Product of Diamonds 
     
Which means in the example pattern the Score is :
= 123–6+456–120+789–504+147–28+258–80+369–162–45–105–189–384
=519

Find the Pattern for getting the HIGHEST SCORE !

New Invention about Bridge Hands Distribution !

In the Card Game of Bridge 13 cards out of 52 are dealt to a Player.

They contain Suits Spades, Hearts, Diamonds or Clubs and each suit may have 0 – 13 cards with all Suits adding to 13 cards in the hand !

We tried to evaluate the total number of Combinations possible and found that the number is 560 !

Varying the numbers from 0 – 13 as the left most number of the Combination [say Spades holding] we got following :

I give here the summary : number of combinations with the first spot [Spades] having 0,1,2,...,12,13 & the Cumulative total in the last Column !

Interestingly 560 is a great number which is the Sum of the first 14 Triangular Numbers !

1+3+6+10+15+21+28+36+45+55+66+78+91+105 = 560

That is :

   1

+ 1+2

+ 1+2+3

+ 1+2+3+4

+ 1+2+3+4+5

+ 1+2+3+4+5+6

+ 1+2+4+4+5+6+7

+ 1+2+3+4+5+6+7+8

+ 1+2+3+4+5+6+7+8+9

+ 1+2+3+4+5++6+7+8+9+10

+ 1+2+3+4++5+6+7+8+9+10+11

+ 1+2+3+4+5+6+7+8+9+10+11+12

+ 1+2+3+4+5+6+7+8+9+10+11+12+13

+ 1+2+3+4+5+6+7+8+9+10+11+12+13+14

= 560

What a number !

You can call 560 a DOUBLE TRIANGULAR NUMBER  !