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6
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# 3 ,
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P L _ C _ D Clue
THE CORRECT COMBINATION IS 65292. SINCE THE THIRD DIGIT IS THREE LESS THAN THE SECOND, AND THE FOURTH IS FOUR GREATER THAN THE SECOND, THERE ARE ONLY THREE POSSIBLE COMBINATIONS FOR THE SECOND, THIRD AND FOURTH DIGITS. THESE ARE -307-, -418-, AND -529-. WITH THE FIRST DIGIT THREE TIMES THE FIFTH, THE ONLY POSSIBLE COMBINATIONS FOR THE FIRST AND FIFTH DIGITS ARE 0 0,3 1, 6 2, AND 9 3. THE SOLUTION ARISES FROM COMBINING THESE TWO SETS OF POSSIBILITIES, WITH THE ADDED CRITERIA THAT THERE ARE THREE COMBINATIONS OF TWO DIGITS THAT THAT EACH SUM TO 11 THE CODE IS 042. BASED ON CLUE #1 AND #2, WE CAN SAY THAT 6 IS NOT THE CORRECT NUMBER. NOW WE KNOW THAT THE UNLOCK CODE DOES NOT CONTAIN 6 AND BASED ON CLUE #3, WE KNOW THAT 2 AND 0 ARE CORRECT NUMBERS BUT IN THE WRONG POSITION. FROM CLUE #1, 2'S POSITION SHOULD BE ON THE RIGHT. THE CODE IS ??2. BASED ON CLUE #5, 0'S POSITION SHOULD BE ON THE LEFT. THE CODE IS 0?2. WE HAVE TO FIND THE MISSING NUMBER IN THE MIDDLE POSITION. BASED ON CLUE #2, THE MIDDLE NUMBER HAS TO BE 4. IT CANNOT BE 1, AS THE STATEMENT SAYS THAT THE NUMBER IS WRONGLY PLACED THE GOLD KEY WILL OPEN THE LOCK. THE CLUE SAYS "A GOLDEN KEY CAN OPEN ANY DOOR". DECIPHER THE MESSAGE BY TAKING THE FIRST LETTER OF EACH WORD, THEN THE SECOND LETTER OF EACH WORD, THEN THE THIRD LETTER AND SO ON TO CONSTRUCT THE SENTENCE THE SECRET CODE IS 7,4,6,5,8. LET THE NUMBERS = A, B, C, D, E BASED ON 1ST CLUE: E + C = 14 BASED ON 2ND CLUE: A = 2B - 1 BASED ON 3RD CLUE: D = B + 1 BASED ON 4TH CLUE: B + C = 10 BASED ON 5TH CLUE: A + B + C + D + E = 30 ALL NUMBERS CAN BE REPRESENTED BY B EXCEPT FOR E SO WE NEED TO REWRITE EQUATION 1. SUBSTITUTE C = 10 - B FROM EQUATION 4 INTO EQUATION 1. E + (10 - B) = 14 E = B + 4 SUBSTITUTE A,C,D,E IN EQUATION 5 (2B - 1) + B + (10 - B) + (B + 1) + (B + 4) = 30 SOLVING FOR B GIVES 4. USE THE OTHER EQUATIONS TO FIND THE VALUES OF A,C,D AND E