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
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 THERE ARE 40 HOUSES. THERE ARE 16 HOUSES BETWEEN NUMBER 12 AND NUMBER 29. SINCE HALF OF THOSE HAVE TO BE ON EACH SIDE, THERE ARE 8 MORE HOUSES ON EACH SIDE. THIS MAKES THE LAST HOME ON ONE SIDE HOUSE NUMBER 20, AND THERE MUST BE 20 MORE HOMES GOING BACK UP THE STREET, WHICH MAKES»A TOTAL OF 40 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