R _ T _ T _
B _ L L
9
T _
M _ K _
_ N T _
_
6 .
P L _ C _
T H _
B _ L L S
6 ,
1 1
_ N D
1 3
T _
G _ T
_
S _ M
_ F
3 0 .
A L L
T H _
N _ M B _ R S
_ R _
_ D D .
T H _ R _
_ S
N _
W _ Y
T _
G _ T
_ N
_ V _ N
N _ M B _ R ,
3 0 ,
B Y
S _ M M _ N G
T H R _ _
_ D D
N _ M B _ R S
T _ G _ T H _ R .
A T
L _ _ S T
_ N _
_ V _ N
N _ M B _ R
_ S
R _ Q _ _ R _ D Clue
ROTATE BALL 9 TO MAKE INTO A 6. PLACE THE BALLS 6, 11 AND 13 TO GET A SUM OF 30. ALL THE NUMBERS ARE ODD. THERE IS NO WAY TO GET AN EVEN NUMBER, 30, BY SUMMING THREE ODD NUMBERS TOGETHER. AT LEAST ONE EVEN NUMBER IS REQUIRED 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 PROFESSOR HAS TO ADD THE REST OF THE DIGITS, FIND THE NEAREST NUMBER TO THE SUM THAT IS DIVISIBLE BY 9 AND GET THE DIFFERENCE. SO, JOHN GAVE THE NUMBER 9646 TO THE PROFESSOR. THE PROFESSOR WILL ADD THE NUMBERS (9 + 6 + 4 + 6) TO GET 25. THE NEAREST NUMBER TO 25 THAT IS DIVISIBLE BY 9 IS 27. AND THE CROSSED OUT NUMBER IS 27 - 25. THIS IS A MATHS TRICK THAT RELIES ON THE POWER OF 9 THE NUMBERS CAN BE GROUPED BY PAIRS: 999,999,999 AND 0; 999,999,998 AND 1′ 999,999,997 AND 2; AND SO ON.... THERE ARE HALF A BILLION PAIRS, AND THE SUM OF THE DIGITS IN EACH PAIR IS 81. THE DIGITS IN THE UNPAIRED NUMBER, 1,000,000,000, ADD TO 1. THEN: (500,000,000 X 81) + 1= 40,500,000,001