A Little Math Puzzle -

[einstein9]

Dear Guys, here is something which i had worked when i was studying, i got this Puzzle from one of the Famous Japanese Math books where the author was 34y and made it for us.

it might be impossible to solve, but believe it or not, i found 3 solutions for it.
and wanted to share it with you here.

the author claims that if you do know how to solve this 4x4 you may solve even 8x8
the rules are simple inside the PDF


PM for Solutions or you may leave it here for all of us,

Good Luck for those WHO WILL TRY


note: forget about my old email on that files

Attachments

Puzzle_Rules.pdf

(9.26 KiB) Downloaded 763 times

[einstein9]

i can see only Downloaded 7 times who where intrested on MATH
i guess only 7 + 1 (me) loves Mathematics,

the rest are BUSY in their DR heheheh

[thatdastardlytech]

This looks real cool! When I have more free time, this looks like a great way to keep my mind engaged!

[einstein9]

good luck glad we added 1 more 2 the list

[nzo17]

PM sent

[einstein9]

A + E+ I + M not equal to 34

chk the formulas


IT IS NOT AS EASY AS IT LOOKS

[nzo17]

A:1
E:12
I:15
M:6


this is 34 right?

[_dex_]

Since you found only 3 solutions then must be you solving this like SUDOKU?

Anyway.
It is some kind of overdefined linear equations.

If we look tere are four 4*4 matices and one 4*2.
Solving it, we can get more and more equations and all are in relation of two sum over other two like:

c+d = e+f
a+b = g+h ,etc...

a+m = h+l
d+p = e+i ,etc...

b+e = k+p
c+h = j+m, etc...

So, there is still too much combinations to solve problem.
But we can reduce it by using maximum enthropy.

1.)
Since we have matrice with numbers from 1-16 without repetition then
we have 8 pairs.
2.)
Max. ent. for sum of two number is sum of all number/number of pairs:
16*(16+1)/2/8 = 17
so, ideal pairs are:
1+16 =17
2+15 =17
3+14 =17
4+13 =17
5+12 =17
6+11 =17
7+10 =17
8+9 =17

Note that in case of position in matrice numbers can be swaped and for case of max entropy
there will be 50-50%

Also for first matrice we can assume that for max.entropy a+b tend to be c+d etc...
so a+b+c+d = 17+17 = 34!!! For solving this problem you DONT have to tell as that
sum of matrices is 34!!! it is obvious.

Using this we have solved 1st and 3th matrice!!! and reduce other to 4*2 matrice.
You can solve that. In this case there is basic solution.

1,16,x,x
x,x,x,x
x,x,x,x
x,x,x,x

1,16,x,x
x,x,x,x
x,x,x,x
x,x,2,15

1,16,x,x
x,x,x,x
x,x,x,x
14,3,2,15

1,16,13,4
x,x,x,x
x,x,x,x
14,3,2,15

1,16,13,4
x,x,x,x
x,x,12,5
14,3,2,15

1,16,13,4
11,6,x,x
x,x,12,5
14,3,2,15

1,16,13,4
11,6,7,10
x,x,12,5
14,3,2,15

and finaly:

1,16,13,4
11,6,7,10
8,9,12,5
14,3,2,15

NOW if you already solved all matrices and you have all pairs relations you can by permutation
to find lots and lots other solution. example:

a+b = g+h
c+d = e+f
i+j = o+p
k+l = m+n

you can write:

7,10,11,6
13,4,1,16
12,15,14,3
12,5,8,9

etc,etc,etc...

B.R.

Dejan