One of the major findings of the Greece-2021 Technology Foresight project concerns a multiple innovation blockage phenomenon, affecting strategic sectors of the national economy and society. To analyse and abate this predicament, the organisers of the end-ofproject Conference put together a game-like experiment, asking students and other participants to think innovatively by answering the question Bin how many ways can you peel an apple?^. The surprising results have verified the expectations from the test. The list of the more than 100 replies received is dominated by very innovative, especially mid-to-high-tech (50%), as well as unconventional, such as lateral thinking (10-20%) ones, whereas the low-to-mid tech responses (less than 1/3 of the total) appear to cover functional niches. The results are assessed with the help of a transpersonal psychology model distinguishing three levels of intelligence; foresight acts at all three levels, but with priority on the highest level, where cultural, ethical and other valuesetting issues are determined.