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Chocolate Bunnies

A candy maker manufactures 7 Chocolate Easter bunnies of increasing sizes.
His plan was to use 10 grams of chocolate for the first bunny he made and 10
additional grams for each of the successive ones. So, at the end, the bunnies
should weigh 10, 20, 30, 40, 50, 60, and 70 grams respectively. However,
after making the first k bunnies, he takes a lunch break and during that time a
mischievous helper messes up his scale so at the end, the remaining 7-k bunnies
wind up weighing 10 grams more than they should. Suppose that you are to
determine when he went out to lunch by means of a [balance]
scale with 3 outputs; less than, equal, and greater than.
- What is the minimum number of weighings you need to determine k?
- Construct a scheme of weighings which achieves this minimum.
- What if there are originally eight bunnies (10 through 80)?

Here are a few clarifications from reader's questions: There are only
seven bunnies, made in order (10, 20, etc.). 'k' can be any number from
0 to 7.
Source:
Univ of Calif, San Diego, Math 187 (Cryptography)
Puzzle #3

Solution

Mail to Ken