Minimal average cost of searching for a counterfeit coin: Restricted model

The following restricted model of coin-weighing problem is considered: there is a heavier coin in a set of n   coins, n-1n-1 of which are good coins having the same weight. The test device is a two-arms balance scale and each test-set is of the form A:BA:B with |A|=|B|⩽ℓ|A|=|B|⩽ℓ, where ℓ⩾1ℓ⩾1 is a given integer. We present an optimal sequential algorithm requiring the minimal average cost of weighings when the probability distribution on the coin set is uniform distribution.