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 Connnected Construction (Posted on 2013-09-13)
```                     +--+
|  |
+--+
/ \
/   \
/     \
/       \
/         \
/           \
/             \
/               \
+--+              +--+
|  |              |  |
+--+              +--+
/|\                /|
/ | \              / |
/  |  \            /  |
/   |   \          /   |
/    |    \        /    |
/     |     \      /     |
/      |      \    /      |
/       |       \  /       |
+--+     +--+      +--+     +--+
|  |     |  |      |  |     |  |
+--+     +--+      +--+     +--+```
Using the digits from 1 to 9 exactly once, construct 7 positive integers so that each positive integer is equal to the sum of the positive integers in the squares that are connected to it from below. Some of these seven positive integers can contain more than one digit.

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution Comment 2 of 2 |

DEFDBL A-Z
CLS
FOR a = 1 TO 9
FOR b = 1 TO 9
IF b <> a THEN
FOR c = 1 TO 9
IF c <> a AND c <> b THEN
FOR d = 1 TO 9
IF d <> a AND d <> b AND d <> c THEN
e = a + b + c
f = c + d
g = e + f
concat\$ = LTRIM\$(STR\$(a)) + LTRIM\$(STR\$(b)) + LTRIM\$(STR\$(c)) + LTRIM\$(STR\$(d)) + LTRIM\$(STR\$(e)) + LTRIM\$(STR\$(f)) + LTRIM\$(STR\$(g))
good = 1
FOR i = 1 TO LEN(concat\$) - 1
IF INSTR(MID\$(concat\$, i + 1), MID\$(concat\$, i, 1)) > 0 THEN good = 0
NEXT
IF LEN(concat\$) <> 9 THEN good = 0
IF good THEN
PRINT g
PRINT e; f
PRINT a; b; c; d
PRINT
END IF
END IF
NEXT
END IF  'c<>a or b
NEXT
END IF  ' b<>a
NEXT
NEXT

finds these solutions

25
18  7
6  9  3  4

25
18  7
9  6  3  4

as, of course, the two bottom-left figures are interchangeable.

Only single-digit numbers needed to be tested on the bottom row, as 2-digit numbers would propagate upward to make 2-digit numbers on all three levels while only two 2-digit numbers can be accommodated while using only nine digits in total.

 Posted by Charlie on 2013-09-13 12:24:44

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