Printing Error:
First observe that 79 can only be 9x8+7 in some order, and with two
of those numbers unavailable, 80 can only be 8x2x5 in some order, so
we can place the 8. If the 9 goes at the bottom, 31 can only be 4+3x9
but 1, 6, and 7 cannot make 27 so this is wrong and 7 goes at the bottom.
Now 31 can be 4x6+7 or 3+4x7. 27 can be 1x3x9 or 3x6+9. The only way
to avoid duplication is to use the first of each pair of possibilities.
We still have to properly order the first two numbers of each row.
9 can be made as 3+2+4, 1+2+6, 1+2x4, or 1x5+4. 21 can be made as
3x5+6 or 1+5x4. Only 3x5+6 and 1+2x4 avoid duplication.
3 x 1 x 9 =27
x + x
5 x 2 x 8 =80
+ x +
6 x 4 + 7 =31
= = =
21 9 79
Joseph DeVincentis
-------------------------------------------------
Here's a solution I found to this puzzle:
3 x 1 x 9
+ + +
5 x 2 x 8
x + +
4 x 6 + 7
In case the ascii formatting doesn't work, here's what i have, row by row:
"3 times 1 times 9 row
plus plus plus row
5 times 2 times 8 row
times plus plus row
4 times 6 plus 7"
Thanks for your time,
Joey
------------------------------------------------
3 * 1 * 9 =27
* + *
5 * 2 * 8 =80
+ * +
6 * 4 + 7 =31
= = =
21 9 79
John Dalbec
------------------------------------------------
Hi Ed,
Here's a solution to Bryce Herdt's Printing Problem problem.
3 * 1 * 9 = 27
* + +
5 * 2 * 8 = 80
+ * +
6 * 4 + 7 = 31
= = =
21 9 79
Thanks again to you and Bryce for the entertainment, Matt Sheppeck
------------------------------------------------
Hi Ed,
This little puzzle stumped me for a while.
However, 80 can be assembled only with
the 5*2*8 and then 79 has only one solution
also.
3 * 1 * 9
* + *
5 * 2 * 8
+ * +
6 * 4 + 7
Dick Saunders Jr.
-------------------------------------------------
Solution:
3 x 1 x 9 = 27
x + x
5 x 2 x 8 = 80
+ x +
6 x 4 + 7 = 31
= = =
21 9 79
Alan Lemm
--------------------------------------------------
3 * 1 * 9 =27
* + *
5 * 2 * 8 =80
+ * +
6 * 4 + 7 =31
= = =
21 9 79
This assumes normal operator precedence of * before +
Kirk Bresniker
--------------------------------------------------
In rows: 3x1x9=27
5x2x8=80
6x4+7=31
In columns: 3x5+6=21
1+2x4=9
6x4+7=1
Simple but ingenious because pleasant for solving - logically, step by step.
Congratulations!
Marek Penszko
Warsaw, Poland
---------------------------------------------------
Printing Error Answer:
3x1x9
x + x
5x2x8
+ x +
6x4x7
Colin Sturm
Michael Matlock
---------------------------------------------------
I don't know if the formating will work, but here are the equations
Verticle from left to right:
(3 * 5) + 6 = 21
1 + (2 * 4) = 9
(9 * 8) + 7 = 79
Horizontal from top to bottom:
3 * 1 * 9 = 27
5 * 2 * 8 = 80
(6 * 4) + 7 = 31
So the grid looks like:
319
528
647
and the operations
* *
* + *
* *
+ * +
* +
Christopher Johnson
------------------------------------------------------
3 * 1 * 9 = 27
* + *
5 * 2 * 8 = 80
+ * +
6 * 4 + 7 = 31
= = =
21 9 79
Wang Zirui
------------------------------------------------------
Hi Ed,
Here's the solution to Bryce Herdt's puzzle:
3 x 1 x 9
x + x
5 x 2 x 8
+ x +
6 x 4 + 7
Daniel Scher