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
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Sign up to join this communityCan 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
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
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.
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.