perplexus.info :: Just Math : The slug and the snail

The slug and the snail (Posted on 2008-10-27)

A slug and a snail decided to settle a long-standing argument as to who was the best sprinter. So they planned a race between two stones set a distance D cm apart. Said the slug to the snail:

- "Since I'm slimier than you, I intend to start T seconds before you".

- "In that case," said the snail, who was rather slow, "I'm going to give you X cm start" (the snail stays at the stone, and the slug starts from X cm ahead.)

It didn't matter. The slug, who could move at speed V cm/sec, was only half as fast as the snail. The result was a dead heat, t seconds after the slug set off.

Now, D, t, T, V and X were all whole numbers from 1 to 10 inclusive, no two numbers being the same.

How long did it take the snail to reach the finish?

See The Solution Submitted by pcbouhid

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re: a solution

| Comment 2 of 7 |

(In reply to a solution by Dej Mar)

There are two sets of values for the five variables, that both lead to the same travel time (t - T) = 7 - 2 = 8 - 3 = 5 seconds for the snail:

 D  t  T  V  X   
10  7  2  1  3    
10  8  3  1  2

The program would find any solution, so the above two sets exhaust the possibilities.

FOR d = 1 TO 10

taken(d) = 1

FOR smt = 1 TO 10

IF taken(smt) = 0 THEN

taken(smt) = 1

FOR t = 1 TO 10

IF taken(t) = 0 THEN

taken(t) = 1

FOR v = 1 TO 10

IF taken(v) = 0 THEN

taken(v) = 1

FOR x = 1 TO 10

IF taken(x) = 0 THEN

taken(x) = 1

IF smt = (d - x) / v THEN

IF (smt - t) = d / (2 * v) THEN

PRINT d; smt; t; v; x

END IF

taken(x) = 0

END IF

NEXT x

taken(v) = 0

END IF

NEXT v

taken(t) = 0

END IF

NEXT t

taken(smt) = 0

END IF

NEXT smt

taken(d) = 0

NEXT d

Edited on October 27, 2008, 11:08 pm

Edited on October 28, 2008, 9:58 am

Posted by Charlie on 2008-10-27 23:06:37

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