on page 155 of 'the mammoth book of new iq puzzles'
a fake coin puzzle asks for the minimum number of weighings on a scale required
to identify a counterfeit silver coin in a group of eight of them
on page 163 the answer is given as 3
but would it not be 2
if 3 coins are placed on each side and one held in each hand
all 8 are accounted for
if the scale is in balance the fake must then be held in one of the hands
remove the 6 coins from the scale and put the hand held coins one on each side
'whichever side it tilts to' (quoting the book answer) will show the fake
two weighings total
alternately if the original weighing of 6 coins is not in balance
whichever side the scale tilts to contains the fake
set down the two hand held coins and remove the 3 coins from the
tilted up side - these 5 coins weigh the same
of the three coins remaining on the scale move one to the other side
taking the third in your hand
if the scale balances the fake is in your hand
if the scales tilts the fake is on 'whichever side it tilts to'
again two weighings total
the problem as written in the book states it is unknown whether the counterfeit is lighter or heavier
but the answer's wording of 'whichever side it tilts to' seems to point toward it being heavier
regardless the two weighing method accomplishes the same result as the three weighing one does, no?
im easily confused so if the two step method is in error please feel free to correct it
the book overall provides a useful means to kill some time while keeping one's brain engaged
a somewhat repetitive format of puzzles but on an increasing scale of difficulty
the book waits to the last two chapters (12 overall) to provide detailed answers
but if youre like me solutions would have been welcomed in every chapter
oh well
still it is a collection of puzzles that does provide mental calisthenics as a way of warding off boredom
and for those of us so afflicted that's not a bad thing