A friend told me to solve TOUGH+TOUGH+TOUGH+TOUGH=PUZZLE, and when I asked for some help, he told me that even if he let me know any of the digits of PUZZLE, I wouldn't be able to solve this. I'm glad he's not an expert in Logic, because what he told me let me deduce the solution. What's the answer?

This metalogic puzzle is entirely the work of Federico Kereki, to whom all credit goes.

The possible solutions, before any clue, are:

4 * 37524 = 150096
4 * 79152 = 316608
4 * 80294 = 321176
4 * 87524 = 350096
4 * 92785 = 371140
4 * 94715 = 378860

My first interpretation of what your friend told you is that even if he said "There is a 'n' in PUZZLE", where n stands for any particular digit, regardless of what digit was chosen, it would not help you.

But each of the following has all non-unique digits:

150096
316608
350096
378860 (the 7 being in one of the other solutions)

So you must have luckily guessed that what he meant was that if he told you what digit any given letter stood for in PUZZLE, you still wouldn't be able to solve it.

This leaves uniquely 350096 for PUZZLE (and 87524 for TOUGH), as P stands for 3 in five of the solutions and U stands for 5, Z for 0, L for 9 and E for 6 in two solutions (the same two solutions in fact, for each), while all the other solutions have at least one letter that would give away the answer if you knew what it stood for.

 

FOR t = 1 TO 9
taken(t) = 1

FOR o = 0 TO 9
IF taken(o) = 0 THEN
 taken(o) = 1

FOR u = 0 TO 9
IF taken(u) = 0 THEN
 taken(u) = 1

FOR g = 0 TO 9
IF taken(g) = 0 THEN
 taken(g) = 1

FOR h = 0 TO 9
IF taken(h) = 0 THEN
 taken(h) = 1

FOR p = 1 TO 9
IF taken(p) = 0 THEN
 taken(p) = 1

FOR z = 0 TO 9
IF taken(z) = 0 THEN
 taken(z) = 1

FOR l = 0 TO 9
IF taken(l) = 0 THEN
 taken(l) = 1

FOR e = 0 TO 9
IF taken(e) = 0 THEN
 taken(e) = 1

tough = t * 10000 + o * 1000 + u * 100 + g * 10 + h
puzzle = p * 100000 + u * 10000 + z * 1100 + l * 10 + e

IF 4 * tough = puzzle THEN
  PRINT  4; "*"; tough; "="; puzzle
END IF

 taken(e) = 0
END IF
NEXT

 taken(l) = 0
END IF
NEXT

 taken(z) = 0
END IF
NEXT

 taken(p) = 0
END IF
NEXT

 taken(h) = 0
END IF
NEXT

 taken(g) = 0
END IF
NEXT

 taken(u) = 0
END IF
NEXT

 taken(o) = 0
END IF
NEXT

taken(t) = 0
NEXT

 

 

Posted by Charlie on 2007-08-16 11:18:05