Answer
There are more 2's because of the numbers beginning with 20,000.
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Puzzle 18
Place JANUARY, FEBRUARY, MARCH, APRIL, MAY, JUNE, JULY, AUGUST, SEPTEMBER, OCTOBER, NOVEMBER, DECEMBER, into the grid. The sequence will snake around, but cannot go diagonally, nor cross itself.
Here is a snippet of section D of the curious multiple-choice entrance exam into the exclusive BrainBashers puzzle club.
Q1. Which is the first question where c) is the correct answer?
a) Q3
b) Q4
c) Q1
d) Q2
Q2. Which is the first question where a) is the correct answer?
a) Q4
b) Q2
c) Q3
d) Q1
Q3. Which is the first question where d) is the correct answer?
a) Q1
b) Q2
c) Q4
d) Q3
Q4. Which is the first question where b) is the correct answer?
Reasoning
Let's look at Q1 first, and check each possible option:
If Q1's answer was a):
… we'll leave checking this for now, because …
If Q1's answer was b):
… we'll leave checking this for now, because …
If Q1's answer was c):
it would reference itself, and we'd learn nothing new, and we'd then have to check Q2.
So, let's start with Q2 first instead of Q1.
If Q2's answer was a):
an immediate contradiction, as Q4 can't be the first answer with a) as we've assumed Q2's answer is a).
If Q2's answer was b):
an immediate contradiction, as Q2 can't be the first answer with a) as we've assumed Q2's answer is b).
If Q2's answer was c):
Q3's answer would be a)
Q1's answer would be d)
confirming Q2's answer as c)
leaving Q4's only possible answer as b)
no contradiction.
If Q2's answer was d):
Q1's answer would be a) (*)
Q3's answer would be c)
Q4's answer would be d)
Q1's answer would be b)
but this contradicts the section marked (*).
Therefore, the only possible answer with no contradiction is when Q2's answer is c).
We can then follow Q2's answer, which leads to the answers to Q1 to Q3. Q4 must then reference itself.
During the recent BrainBashers school sports day, four students were competing in the 400 metres hurdles.
Official figures mysteriously went missing just after the event, however, various spectators could remember the following information.
Alex won and wore red. The student wearing number 1 came third. Billie beat the student in yellow, but wasn't wearing number 2. Only one student finished in the same position as the number they wore, but they didn't wear red. Emery beat the student wearing number 3, and Glen wore yellow. The student in green wore number 2. A spectator remembered that one student wore blue, but couldn't remember anything else about them.
Can you determine the positions the students finished in, along with the numbers and colours they wore?
Answer # Name Wore Colour
1 Alex 4 Red
2 Emery 2 Green
3 Billie 1 Blue
4 Glen 3 Yellow
Reasoning
(Clue 1) Alex won and wore Red. (Clue 5) Glen wore Yellow. (Clue 3) Billie wasn't wearing number 2, and (Clue 6) number 2 wore Green, so must be Emery. Leaving Billie in Blue. # Name Wore Colour
1 Alex Red
? Glen Yellow
? Emery 2 Green
? Billie Blue
(Clue 2) Emery didn't come 3rd, and Alex won, so (Clue 5) Emery can't have come last, so must have come 2nd. # Name Wore Colour
1 Alex Red
2 Emery 2 Green
? Glen Yellow
? Billie Blue
(Clue 3) Billie can't have been last, so came 3rd and (Clue 2) wore 1, leaving Glen in last place. # Name Wore Colour
1 Alex Red
2 Emery 2 Green
3 Billie 1 Blue
4 Glen Yellow
(Clue 5) Emery beat the student wearing 3, so Glen must have worn 3. Leaving Alex wearing 4. # Name Wore Colour
1 Alex 4 Red
2 Emery 2 Green
3 Billie 1 Blue
4 Glen 3 Yellow
