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March 3, 2015

March 3, 2015

Posted by **Mark** on Monday, July 8, 2013 at 6:58pm.

- Math (please help me Steve) -
**MathMate**, Tuesday, July 9, 2013 at 6:51amHere's a lower bound solution. You may want to investigate other possibilities.

The number 7 can be partitioned into 3 ascending non-negative integers in 8 ways, namely:

007#

016

025

034

115#

124

133#

233#

There are 3 permutations of partitions (indicated #) with non-distinct digits and 6 permutations of those with distinct digits for a total of

4*3+4*6=36 permutations of non-negative integers whose sum is 7.

Each of these permutations can make a 3x3 grid as follows by putting a permutation as the first line, then rotate the digits to the left:

124

241

412

We can also make another grid by rotating them to the right, as follows:

124

412

241

This doubles the number of grids for a total of

36*2=72 grids.

- Math (please help me Steve) -
**math**, Wednesday, July 10, 2013 at 6:36amwhat about this case, i didnt enumerated it

1 2 4

0 5 2

6 0 1

- Math (please help me Steve) -
**exactly**, Sunday, September 22, 2013 at 1:47amHint: you need these:

(1) a,b,c,d are non-negative integers

(2) 7−a−b≥0⇔a+b≤7

(3) 7−c−d≥0⇔c+d≤7

(4) 7−a−c≥0⇔a+c≤7

(5) 7−b−d≥0⇔b+d≤7

(6) a+b+c+d−7≥0⇔a+b+c+d≥7

Try to count how many satisfies these conditions (:

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