MathDB

Georgina calls a

992

-element subset

A

of the set

S = \{1, 2, 3, \ldots , 1984\}

a halfthink set if
[*] the sum of the elements in

A

is equal to half of the sum of the elements in

S

, and [*] exactly one pair of elements in

A

differs by

1

.
She notices that for some values of

n

, with

n

a positive integer between

1

and

1983

, inclusive, there are no halfthink sets containing both

n

and

n+1

. Find the last three digits of the product of all possible values of

n

.
Proposed by Andrew Wu and Jason Wang
(Note: wording changed from original to specify what

n

can be.)

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