perplexus.info :: Just Math : Number Rectangle

Number Rectangle (Posted on 2004-01-08)

Place twelve of the numbers 1 to 15 in the grid below such that:
1. The rows (a,b,c,d; e,f,g,h; i,j,k,l) have the same sum.
2. The columns (a,e,i; b,f,j; c,g,k; d,h,l) and the diagonals (a,f,k; b,g,l; c,f,i; d,g,j) all have the same sum.
Note: The rows do not have the same sum as the columns and diagonals.

a|b|c|d
-+-+-+-  
e|f|g|h
-+-+-+-
i|j|k|l

Submitted by Brian Smith

Rating: 4.5000 (2 votes)

Solution: (Hide)

There are two solutions (excluding rotations and reflections) using 12 numbers 1-15, both of which can be expressed by a general solution in three variables.
9 3 13 7 12 2 14 4 2a+3b+k b+k 2a+5b+k 3b+k 14 10 6 2 11 9 7 5 a+6b+k a+4b+k a+2b+k a +k 1 11 5 15 1 13 3 15 k 2a+4b+k 2b+k 2a+6b+k k=1,a=1,b=2 k=1,a=4,b=1

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-02-16 07:48:05
answer	K Sengupta	2007-09-11 03:58:33
solution	SilverKnight	2004-01-08 20:06:47
Is this even possible?	SilverKnight	2004-01-08 19:18:18

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