Shortcuts to Accidents

We saw cognitive reflection problems, where our mind (brain) wants us to lock in – what it believes to be – a ‘timely’ answer which it gets via mental shortcuts. Here is one such question

Fill the box with the question mark to make the accidents in two roads equivalent.

Studies have shown a high proportion of people answered 8. Their attempt was perhaps to maintain the same ratio (2000:16 == 1000:8). But the question was to estimate the number of minor incidents required for a road with fewer major accidents to make it equivalent to the one with more major accidents. Naturally, it should be much more than 1000 (the shortfall of major accidents on Road 2 vs Road 1).

Cars and workers

Another famous trick puzzle has the following form:

It takes 7 workers to make 7 cars in 7 days. How many days would it take 5 workers to make 5 cars?

Park your instincts to answer 5 (so that 5-5-5 matches with 7-7-7!) for a while. Try this first,
If 7 workers can build 4 cars in 3 days, how many days would it take 8 workers to build 6 cars??
I assume more people answer the second one correctly because it shows fewer visible patterns and may slow you down.

Answer: car per worker per day = (4/7)/3 = 4/21. So, 8 workers can make 32/21 cars in a day. But we want 6 cars => (32/21) x X (days) = 6. X = (21 x 6)/32 = 3.9 days.

In the same way, the first question is answered as follows:
(7/7)/7 = 1/7 car per worker per day. 5 workers can make 5/7 cars in a day. For making 5 cars, one needs (5/7) x X (days) = 5 or X = 35/5 = 7 days.