Hello Viewers

Time for another figure-crunching again.

Produce a 64-square diagram. Fill in the squares with numerals 1 – 64 to obtain the same sum on all vertical, horizontal, and the 2 diagonal lines. Each number may be used only once. All 64 numerals must be used.

Good luck.


ps. Such a silly error in the opening sentence. My apologies.

haha, geo

You made it! Too bad I am not good at numbers......

Hello Alexia

You'll never succeed if you don't even try. Make an attempt. I can provide clues if so required

Quote:

Hello 美人

Okay, okay! I’ll do it again.

Hey Viewers.

It’s time again for a solution to Matrix Arithmetic II.

Construct a 64-square diagram. Fill in the squares with numerals 1 ~ 64 to obtain the same overall total sum on all vertical, horizontal, and the 2 diagonal lines. Each number may be used only once. All 64 numerals must be used.

Good luck.

06 61 04 59 08 63 02 57
60 03 62 05 58 01 64 07
53 14 51 12 55 16 49 10
11 52 13 54 09 50 15 56
46 21 44 19 48 23 42 17
20 43 22 45 18 41 24 47
29 38 27 36 31 40 25 34
35 28 37 30 33 26 39 32
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==> http://www.answers.com/magic%20square

Hi Lady,

Congratulations! It's YOU again. Brilliant.

From the link provided, I can see two different solutions to my riddle.

I have a third solution that is proprietary to me. Wanna attempt?

Working on it. Any hints?

Hi Lady Futari
& all others interested in this riddle

Sure! I have sent Tim an email with attachment showing the clues to this riddle.

Just a little patience, please.

Cheers.

geo

Hi Futari & All Viewers interested in this thread.

Tim must be busy, so I thought I do it manually here.

Here are some clues...

There’s no secret to my formula; just some hard thinking that’s all.

Firstly, position the 64 numbers in running sequence as illustrated below.

01 02 03 04 05 06 07 08 = 036
09 10 11 12 13 14 15 16 = 100
17 18 19 20 21 22 23 24 = 164
25 26 27 28 29 30 31 32 = 228
33 34 35 36 37 38 39 40 = 292
41 42 43 44 45 46 47 48 = 356
49 50 51 52 53 54 55 56 = 420
57 58 59 60 61 62 63 64 = 484

232 240 248 256 264 272 280 288 = 2,080÷8
= 260

You will find that all the numbers add up to 2,080. The Magic Constant of 260 is derived by dividing the sum by 8 (Order 8 as it is called).

Secondly, by arranging the numbers in the sequence as shown, each of the sum of the two individual diagonal lines supernaturally add up to the Magic Constant of 260. This means to say that those numbers in the two diagonal lines stay put.

Over to you and all those interested. Shouldn’t be too difficult from here. Just juggle the numbers here and there, and you will have the solution.

Cheers.

geo