Question 1036710: 0,3,8,60,51,62,93,45,?,0,120,440,960
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
0,3,8,60,51,62,93,45,?,0,120,440,960
We notice that the first three terms are 1 less than the
squares 1²,2²,3², but then we ask: what does 60 have to
do with 4²=16? Then it occurs to us that if we reverse
the digits of 16 and subtract 1, we get 61-1=60. So we
try that scheme. When we "reverse the single digit" of a
1-digit number we get the same 1-digit number. That's
why the first three numbers are the same as 1 less than
the squares.
Square 1, get 1
Reverse the single digit, get 1
Subtract 1, get 0.
Square 2, get 4
Reverse the single digit, get 4
Subtract 1, get 3.
Square 3, get 9
Reverse the single digit, get 9
Subtract 1, get 8.
Square 4, get 16
Reverse the digits, get 61
Subtract 1, get 60.
Square 5, get 25
Reverse the digits, get 52
Subtract 1, get 51.
Square 6, get 36
Reverse the digits, get 63
Subtract 1, get 62.
Square 7, get 49
Reverse the digits, get 94
Subtract 1, get 93.
Square 8, get 64
Reverse the digits, get 46
Subtract 1, get 45.
Square 9, get 81
Reverse the digits, get 18
Subtract 1, get 17. <--- that the answer.
But let's keep going
as a check.
Square 10, get 100
Reverse the digits, get 001, or just 1
Subtract 1 get 0
Square 11, get 121
Reverse the digits, get 121
Subtract 1 get 120
Square 12, get 144
Reverse the digits, get 441
Subtract 1 get 440
Square 13, get 169
Reverse the digits, get 961
Subtract 1 get 960
Edwin
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