S _ L _ T _ _ N
F _ R
4
N _ M B _ R S :
1
+
1
+
2
+
4 =
1
X
1
X
2
X
4 .
S _ L _ T _ _ N
F _ R
5
N _ M B _ R S :
1
+
1
+
1
+
2
+
5 =
1
X
1
X
1
X
2
X
4
1
+
1
+
1
+
3
+
3 =
1
X
1
X
1
X
2
X
4
1
+
1
+ 2
+
2
+
2 =
1
X
1
X
2
X
2
X
2 Clue
IF THE PING-PONG BALL ROLLS FLUSH AGAINST THE WALL, THE CAST-IRON BALL CANNOT CRUSH IT. THOSE WHO KNOW GEOMETRY CAN DETERMINE THAT IF THE DIAMETER OF A LARGE BALL IS AT LEAST 5.83 (3+2(SQUARE ROOT OF 2) TIMES AS LARGE AS THE DIAMETER OF A LITTLE BALL, THEN THE LITTLE BALL WILL BE SAFE IF IT HUGS THE WALL. A CAST-IRON BALL THAT IS LARGER THAN A SOCCER BALL IS MORE THAN 4.83 TIMES AS LARGE IN DIAMETER AS A PING-PONG BALL THE BUTLER DID IT. MR. ELLIS KNEW THE BUTLER WAS LYING BECAUSE PAGES 35 AND 36 IN A BOOK ARE ALWAYS PRINTED ON OPPOSITE SIDES OF THE SAME PIECE OF PAPER 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 SOLUTION FOR 4 NUMBERS: 1 + 1 + 2 + 4= 1 X 1 X 2 X 4. SOLUTION FOR 5 NUMBERS: 1 + 1 + 1 + 2 + 5= 1 X 1 X 1 X 2 X 4 1 + 1 + 1 + 3 + 3= 1 X 1 X 1 X 2 X 4 1 + 1 +2 + 2 + 2= 1 X 1 X 2 X 2 X 2