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 Five Mileposts (Posted on 2013-05-31)
On my way to Philadelphia I pass five mileposts that indicate the distance I still have to travel to Philadelphia. The mileposts are at fixed intervals. Each milepost has a two-digit number, and together the five mileposts use all the digits from 0 to 9 exactly once.

(i) What is the smallest distance that the closest milepost can be from Philadelphia?

(ii) What is the maximum distance that the closest milepost can be from Philadelphia?

***Mileposts don't begin with 0, that is, no milepost can contain a leading zero.

 See The Solution Submitted by K Sengupta Rating: 3.0000 (1 votes)

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 solution | Comment 25 of 26 |

The possibilities:

`  distances               separation   98  76  54  32  10          22 90  72  54  36  18          18 94  83  72  61  50          11 90  81  72  63  54          9`

So the closest minimum closest is 10 and the maximum closest is 54.

Found by:

FOR closest = 10 TO 90
max = (100 - closest) / 4
FOR diff = 2 TO max
d(1) = closest
good = 1
d1 = closest \ 10: d2 = closest MOD 10
IF d1 = d2 THEN good = 0
IF good THEN
REDIM used(9)
used(d1) = 1: used(d2) = 1
FOR i = 2 TO 5
d(i) = d(i - 1) + diff
IF d(i) > 99 THEN good = 0: EXIT FOR
d1 = d(i) \ 10: d2 = d(i) MOD 10
IF d1 = d2 THEN good = 0: EXIT FOR
IF used(d1) OR used(d2) THEN good = 0: EXIT FOR
used(d1) = 1: used(d2) = 1
NEXT
IF good THEN
FOR i = 5 TO 1 STEP -1
PRINT d(i);
NEXT: PRINT , diff
END IF
END IF
NEXT
NEXT

 Posted by Charlie on 2013-05-31 12:20:41

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