Determine a list of eight positive integers (not necessarily distinct) such that summing seven of them in all eight possible ways generates only seven distinct results: 418, 420, 423, 424, 426, 428 and 429.
One sum , out of 8 possible , is missing . Denote it by x
Let S8 be the sum of all 8 numbers and S7 of the 7 listed
S7= 418+420+...+429=2968
Clearly c+x= 7*S8 IS DIVISIBLE BY 7
SO X MUST BE DIVISIBLE BY 7, SINCE 2968 IS
X HAS TO BE ONE OF THE NUMBERS LISTED =>> x=420
and S8=3388/7=484
NOW THE 8 NUMERS ARE DERIVED:
484-418=66
484-420=64
484-420=64 THE EXTRA PARTIAL SUM
484-423=61
....ETC
484-429=55
,,,,,,NICE PUZZLE
another way
