+---+ +---+ +---+
| | X | | X | | = 54
+---+ +---+ +---+
X X X
+---+ +---+ +---+
| | X | | X | | = 120
+---+ +---+ +---+
X X X
+---+ +---+ +---+
| | X | | X | | = 56
+---+ +---+ +---+
= = =
96 180 21
Use each of the digits from 1 to 9 exactly once to satisfy this cross product puzzle.
How fast can you come up with the solution using only p&p (no calculator)?
Extra Challenge: Can you come up with the solution in your mind (without using p&p)?
+---+ +---+ +---+
| | X | | X | | = 54 = 2 * 3 * 3 * 3
+---+ +---+ +---+
X X X
+---+ +---+ +---+
| | X | | X | | = 120 = 2 * 2 * 2 * 3 * 5
+---+ +---+ +---+
X X X
+---+ +---+ +---+
| | X | | X | | = 56 = 2 * 2 * 2 * 7
+---+ +---+ +---+
= = =
96 180 21
= = =
2 2 3
* * *
2 2 7
* *
2 3
* *
2 3
* *
2 5
*
3
The only 7 has to be in the lower right corner.
The 9 can go only in the row with more than one 3 intersects just such a column: row 1, column 2.
The 5 must go in the middle row, middle column.
The middle column now needs 4 and it has only the bottom row to put it.
The bottom row now has a 2 to use up and only the first column free to take it.
The last column needs a 3. We can't put it in the top row as that would force a second 2 into column 1. So the last column's 3 must go in the second row, leaving a 1 in its top-row position.
That requires a 6 in the top left.
Then the 8 that remains fits perfectly at the left end of the middle row.
+---+ +---+ +---+
| 6 | X | 9 | X | 1 | = 54 = 2 * 3 * 3 * 3
+---+ +---+ +---+
X X X
+---+ +---+ +---+
| 8 | X | 5 | X | 3 | = 120 = 2 * 2 * 2 * 3 * 5
+---+ +---+ +---+
X X X
+---+ +---+ +---+
| 2 | X | 4 | X | 7 | = 56 = 2 * 2 * 2 * 7
+---+ +---+ +---+
= = =
96 180 21
= = =
2 2 3
* * *
2 2 7
* *
2 3
* *
2 3
* *
2 5
*
3
|
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Posted by Charlie
on 2023-04-24 09:59:13 |
p&p
