Teaser 2511

[Cactus]

Sunday Times Teaser 2511 by Peter Harrison
-----------------------------------------------------------------

I have a number of weights, each a whole number of grams, which, if I
take them in pairs in every possible combination, allows me to weigh
an almost complete sequence of 16 weights with only 100 and 101 grams
missing.

But I can still manage an unbroken sequence of 13 weights with only
one, a prime number, duplicated.

What, in increasing order, are the weights (in grams) of my weights?

Cactus

[Peter]

Good Morning All,

for simplicity I started with the analogous case of 6 different
weights in the range 1 to 11 grams. Adding 42 grams to each of them
gives a sequence of pairs from 87 to 102 grams, excluding 100 and 101
grams. The prime weight 89 grams is duplicated.

Peter

[Garry]

And it's easy to show that the other 14-weight pattern matching the
given conditions, i.e. 99, 102-114, can't be reached by totalling any
6 individual weights (6, since 6C2=15, 15 less one duplicate gives 14
distinct values).

Garry