4
$\begingroup$

Can you place these numbers into 5 rows of 4 such that each row totals 20?

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

$\endgroup$
10
$\begingroup$

Sure.

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

Method:

Started from the bigger numbers, and partitioned into 5 parts of 20: {8,8,4}, {8,7,5} and so on.

Then swapped a big number with two smaller ones (with the same sum) on another row until I had 4 numbers on each row.

With some fiddling, it's also possible to get all the columns to add up to 25:

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

And here's a magic square (with duplicates, unavoidably) followed by a row of fives:

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

And finally:

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

This has
* 20 on all 5 rows
* 20 on all 4 long diagonals
* 25 in all 4 columns
* a magic square on the first 4 rows

| improve this answer | |
$\endgroup$
  • $\begingroup$ I'm late ! But I have differents rows :D $\endgroup$ – Narlore Apr 25 '19 at 8:25
  • $\begingroup$ I like the way you went on to challenge yourself by finding solutions to your own proposed questions. $\endgroup$ – 5202456 Apr 25 '19 at 9:45
  • $\begingroup$ @5202456 Thanks! The original solution seemed to leave an awful lot of "wiggle room" in the pattern, so I wanted to see what I could do with it. I added one more "extra magical" solution after your comment; hopefully I didn't make any mistakes, as the numbers are starting to bounce around in my eyes :-) $\endgroup$ – Bass Apr 25 '19 at 11:08
5
$\begingroup$

A bit late to the party and cannot beat the excellent answer from @Bass.

I worked out the number of distinct solutions bearing in mind they can be further permuted by ordering each row and the row sequence. I found

16 distinct solutions

I did this by first finding all the sets of four digits which sum to 20.

There are 17 sets of digits

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

I then permuted them for each row so that each digit is used the right number of times.

These are the 16 solutions

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

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

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

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

Method:

A computer program written in C.

| improve this answer | |
$\endgroup$
  • $\begingroup$ Nice! FYI I generated the puzzle from row 2 column 4. $\endgroup$ – JMP Apr 25 '19 at 11:28
3
$\begingroup$

This one works

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

Method :

Write randomly the numbers on a piece of paper during 5 min until the solution appears magically.

| improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.