LOGICAL AND ABSTRACT REASONING
When acquiring a new language, logical reasoning in the target language is always a very necessary skill.
It’s why I was looking for some puzzles that could help me to reinforce it. These questions were picked
up from the activities bank of Michael Lewis & Jimmie Hill (their book is available in our library). The
authors recommend the teachers to stimulate their students to discuss, reason, and argue in English
(instead of letting them only to revert to their own language). The proposed activity is appropriate for
students of all levels. Its questions are ordered by their difficulty level and it would be better if you
assign questions with a higher level of difficulty to students of higher levels. All, these questions are
good nil time fillers, if used from times to times.
Question # 1
Three men went out to dinner. The bill was Thirty dollars. Each man gave a ten dollar bill to the waiter.
He took the bill to the office and they said there’d been a mistake. The bill should have been twenty-five
dollars, not thirty. The waiter was supposed to give five dollars back to the men. He realized that the five
was difficult to divide by three, and the men did not really know how much the bill was anyway. So he
kept two dollars for himself and gave a dollar back to each man. That means each man had paid nine
dollars and the waiter had two dollars, but (3 x 9) + 2 = 29, not 30. Where is the other dollar?
Answer:
This ”reasoning” is fallacious; from the initial amount of thirty dollars, the men spent twenty-five dollars
for their meal and two dollars to tip the waiter; the two dollars have to be considered an outcome (with
negative sign ) and not an income (positive sign).
The correct balance is:

From the point of view of the restaurant owner:
$30 – $5 (the change) = $25 (the amount of the bill)

From the point of view of the three men:
$9 x 3 = $27 (the money they gave)
$27 - $2 (the tip) = $25 (the amount of the bill)
Question#2
The fast train leaves A for B at exactly the same time as the slow train leaves B for A. The fast train
travels at 100 km an hour, the slow train at 60 km an hour. Which train is further from A when they
meet?
Answer: are you trying to establish a system of equations in order to determine the distances that have
travelled the fast and the slow trains at the moment of their encounter? Forget about it! You are taking
the wrong way…the datum about the speeds is completely irrelevant. Make a pause and just think for a
moment: the really relevant thing is that both trains left at the same moment; so, when both trains have
their encounter, the fast train has travelled a distance D1 from A; the slow train has travelled a distance
D2, from B. D1 + D2 = D (the distance between A & B). From the slow train’s perspective, the distance to
A is D1, the same distance travelled by the fast train…hehehe!
Question # 3
Two fathers and two sons leave town, but the population only goes down by three. How is that
possible?
Answer: hehehe...a man left the town in company of his son and his grandson and the grandson who
left the town with him is the son of the son that also left the town with him. Confusing! Isn’t it?
Question#4
A man is looking at a picture; he says: “Brothers and sisters I have none, but this man’s father is my
father’s son.” Who is he looking at?
Answer: hehehe…hi’s looking at his own pic! (I am my father’s son --- whether I have or not any sibling)
Question # 5
A woman drove her car one mile to the top of a mountain. Her speed was 20 km an hour. How fast must
she drive one mile down the other side so that the average for the whole (two mile) journey is 40 km an
hour?
Answer: instead complicating the problem with miles to kilometers calculations, let’s consider V as the
speed down the mountain. As the average speed has to be 40 km an hour, we get the following
equation:
(20 km an hour + V) / 2 = 40 km an hour
 V = (2 * 40 km an hour) - 20 km an hour
 V = 80 km an hour - 20 km an hour
 V = 60 km an hour
Question #6
A frog is at the bottom of a 30-meter well. Each hour it climbs three meters and slips back two. How
many hours does it take for it to get out?
Answer: the frog climbs one meter per hour (3 - 2 = 1); from the bottom to the top, there are 30 meters;
so, it will need 30 hours to climb all the height.
Question#7
A clock strikes six in five seconds. How long does it take to strike twelve?
Answer: six strikes correspond to a lapse of five seconds; so, twelve strikes will correspond to a lapse of
ten seconds? No! People make this mistake when solving this quibble; but, as matter of fact, the clock is
about to strike but didn’t do yet, it is five seconds to six hours.
So, the clock is going to strike again in five seconds and another six hours (at twelve hours exactly).