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Old 12th June 2005 | 09:27
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Send Clowns

Jet Blast Rat
 
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From: Sarfend-on-Sea
So you have a series of figures n1 to ni, all single digits, such that n1 + 10n2 +100n3 + ... = 8 x (n1 + n2 + n3 + ...)

= 8 x n1 + 8 x n2 + 8 x n3 + ...

Seeing it like this there is certainly an upper cap, as the multiplication by 8 is eclipsed by the multiplication by 100 of the figure in the third column, and by 1000 of the figure in the 4th column. There must also be a lower limit above 9, as the figure in the first column is a unit, yet multiplied by 8 on the other side of the equation.

Certainly more than 20, to account for the 8s from the 10s column and then some from the units (since 10 itself does not fit except in octal). Certainly less than 100 because all hundreds only give 8 each as any digit does on the other side of the equation, and the maximum units figure is 9, giving 72 which cannot make up for the rest even at 100. Any figure in the 10s column of course only make things worse, giving 10 on the side that is already higher and only 8 again on the other side.

The only options are therefore 24, 32, 40, 48, 56, 64, 72, 80, 88 and 96, the muliples of 8 in this range. The answer is of course 72.
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