The 2026 FIFA World Cup is over, but the next one is always only four years away. This is a good occasion to remind ourselves of India’s ambition to host one of the future World Cups, not to mention a possible bid for an Olympic Games edition in the nearer future.
Imagine that India is indeed hosting a World Cup sometime in the future. We pick up play in the closing stages of the tournament.
#Puzzle 204.1
This puzzle involves only the last five matches in a FIFA World Cup being hosted in India: the last quarter-final (we ignore the first three), the two semifinals, the playoff for third place, and the final. There are a lot of clues on what happens in those matches. But before that, a few disclaimers:
(a) When a clue mentions a team’s first match or second match, it does not its first or second match in the tournament. It simply refers to the team’s first or second match within this set of five games.
(b) “Before” and “after” may or may not refer to consecutive matches, unless explicitly mentioned. If not mentioned, it simply means that one match happened at some time before the other.
(c) “A and B are consecutive” can mean either AB or BA, unless the order is explicitly stated.
{{/usCountry}}(c) “A and B are consecutive” can mean either AB or BA, unless the order is explicitly stated.
{{/usCountry}}(d) “Consecutive” means consecutive matches, but may or may not mean consecutive days. For example, if there is no match on Tuesday, it means the matches on Monday and Wednesday are consecutive.
So, here is the breakdown on what happens in the closing stages:
(1) The last five matches involve five teams: Argentina, Brazil, France, Germany and Spain.
(2) One of these five teams is eliminated on Monday in the last of the four quarter-finals.
(3) The remaining four teams play the semifinals on Wednesday and Thursday.
(4) The semifinal losers play for third place on Saturday.
(5) The final between the semifinal winners takes place on Sunday.
(6) The matches are played in Chennai, Delhi, Hyderabad, Kolkata and Mumbai, in whichever order.
(7) The winners in the five matches score 2, 3, 4, 5 and 6 goals, in whichever order.
(8) The losing teams score 0, 1, 2, 3 and 4 goals, in whichever order.
(9) Two of the five matches are lost by Germany.
(10) The Kolkata match happens after the Mumbai match.
(11) Argentina’s first match comes immediately after France’s first match.
(12) Spain’s defeat comes in either the quarter-final or the final.
(13) Either the quarter-final or the final is won by a team scoring 3 goals.
(14) One of the teams in Saturday’s match is France.
(15) Wednesday’s winner is Brazil.
(16) The Hyderabad match is played before the Delhi match.
(17) Brazil defeat Argentina in the second match for both teams.
(18) The Chennai match comes before the match in which the winner scores 5 goals. After these two comes the match in which the winner scores 2 goals
(19) France’s first match and the Delhi match take place consecutively.
(20) A match won by Argentina and the match in which the loser scores 1 goal are consecutive.
(21) Germany’s first match comes before the match in which the winning team scores 2 goals.
(22) The match with a 6-goal winner comes after the match in which the winner scores 2 goals.
(23) The matches in which the losers score 0 and 3 goals are consecutive, in exactly that order.
(24) Germany’s first defeat comes after the match in which the losing team scores 1 goal.
(25) Argentina’s defeat comes after Germany’s second defeat.
(26) Argentina’s defeat comes after the match in which the winner scores 2 goals. The Chennai match comes before both these matches.
(27) The match in which the winner scores 4 goals and the match in which the loser scores 4 goals are consecutive.
(28) The match in which the loser scores 1 goal and the Delhi match are consecutive.
What are the results of the five matches, including goal scores? (Tabular form not necessary.)
#Puzzle 204.2
Using the key A = 1, B = 2… Z = 26, I looked at the products of the letter values in some of the World Cup teams. Product means INDIA = 9 x 14 x 4 x 9 x 1 = 4536, but India is not a World Cup team.
Even without looking at all 48 teams, it is obvious that the lowest product is 168, and it should not take you long to identify that team. Only one other team appears to yield a three-digit product (784), while two four-digit products are 2268 and 2912.
Identify all four teams.
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 203.1
Hi Kabir,
The distance of the college from the two villages is 9 km (boy) and 8 km (girl). The speeds of the boy and girl are 15 km/h and 20 km/h respectively.
The boy and the girl meet at 9:24 am. The time taken by the boy and the girl to cover an equal distance from there to the college are 12 min and 9 min respectively. Therefore, their speeds are in an inverse ratio, i.e. 3:4 or 3x and 4x respectively.
Overall, the boy travels for 36 min and the girl for 24 min. Therefore,
Distance travelled by the boy = (36/60) (3x) = 9x/5
Distance travelled by the girl = (24/60) (4x) = 8x/5
The difference between the two distances = 1 km (given). Thus, 9x/5 – 8x/5 = 1 => x= 5. This gives 3x = 15 km/h and 4x = 20 km/h. The distances work out to (9x/5) = 9 km, and (8x/5) = 8 km.
— Sabornee Jana, Mumbai
#Puzzle 203.2
Dear Kabir,
Father #1 is the grandfather, giving ₹150 to his Son #1, who is also Father #2. Out of the ₹150 received,
Father #2 gives ₹100 to his Son #2. So Son#1 is left with ₹50 and Son#2 has ₹100. The two sons have together gained ₹150.
— YK Munjal, New Delhi
(This actually works even if Father #2 is the grandfather. Either way, the answer is correct. — KF)
Solved both puzzles: Sabornee Jana (Mumbai), YK Munjal (Delhi), Anil Khanna (Ghaziabad), Dr Sunita Gupta (Delhi), Yadvendra Somra (Sonipat), Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Vinod Mahajan (Delhi), Professor Anshul Kumar (Delhi), Shri Ram Aggarwal (Delhi), Ajay Ashok (Delhi), Shishir Gupta (Indore)