Hello Members & Viewers.

Once again, I am seeking a solution(s) for Matrix Arithmetic III.

Construct a 16-square diagram. Fill in the squares with 16 different numbers choosing from a series of between 1 ~ 48 to obtain a constant total sum of 98 on all vertical, horizontal, and the 2 diagonal lines. No numbers must be repeated.

The 16 different numbers comprise of 2 single digit and 14 double digits. The sum of the 16 numbers is 392.

Good luck.

it is cheating if i do it by matlab programming? sure, i write the program myself

Hello Rony

It doesn't matter what tools or methods you employ to solve the riddle. There are several options to do it. Please post your solution.

Cheers!

that really kills me, i wanted to write some codes to calculate the problem, but after some thoughts, i gave up,cuz even the codes could solve it, it has to calculate billions of times, there must be some other unregular method.

all i got is

32 18 19 29
21 27 26 24
25 23 22 28
20 30 31 17

but obviously, it doesnt completely meet the requiements.
Gimme some more time

Hi Rony

An excellent attempt indeed! I can't say it is wrong except that you have not used the 2 single digit numbers as required of the riddle.

The extremely powerful Matlab application should solve the problem in no more than 5 minutes. On the other hand, try a conventional method using the Excel Solver. It may take about 12 to 15 minutes to solve it.

Some relevant clues here. The 2 single digit numbers are 3 and 5. The highest number used is 46. Four numbers are in their 10's; four in the 20's; four in the 30's and two in the 40's. The numbers occupying the four corners are 3, 22, 35 and 38. These clues are for only one method. There is at least another method that is quite universal.

Good luck pal.

Cheers!

My try:

03 44 13 38
24 27 14 33
36 11 46 05
35 16 25 22

Here's another one:

02 45 12 39
23 28 13 34
37 10 47 04
36 15 26 21

Still looking for the rest of the possibilities.
It's FUN!! But my head is filled with numbers now.

Hi Lady

Brilliant! Sure, there are at least another 2 methods using different numerals. But your first method is 'd' universal method. Congratulations!

Cheers!

seems i'm not smart enough, ><!!

Hi Rony

Lady Futari's first solution like I said is 'd' universal solution. However, she has the positions of the numbers reversed. Of course it is still correct and my only guess why she has done it that way is ... she is left-handed.

Don't depair! Here's another method.

The numbers used are

03, 05, 11, 13
14, 16, 22, 24
25, 27, 33, 35
36, 38, 44, 46

The end result is

03 44 38 13
24 27 33 14
35 16 22 25
36 11 05 46

Note that if you arrange the numbers in sequence (from smallest to the largest as illustrated in the first set of numbers), you find that the two diagonal lines each adds up to 98. In other words, the numbers at the four corners are there to stay.

What is left to be done is

1. to exchange positions of the four centre numbers, i.e. 16 with 27 and 22 with 33.

2. to cross-exchange positions of the remaining eight numbers. 05 takes the place of 44; 11 with 38; 14 with 35; and 24 with 25.

In this way all rows, columns and lines, each adds up to a constant of 98.

I am designing a 64-square Matrix Arithmetic IV to be released at a later date.

Cheers.