March 2026 Challenge

Transportation Survey Puzzle

62 people have taken part in a survey on modes of transport they use to travel to work.

They have been asked whether they travel by Car only, Bus only, Train only or a combination of these three modes of travel. 

1. Twice as many people use the Car only as use the Car and Train only.
2. Four more people use the Bus only than the Train only.
3. Twice as many people use the Train and Bus only, as use all three modes.
4. The same number of people use the Car and Bus only as use the Bus only.
5. Thirteen more people use the Car only than the Bus only.
6. Two people use all three modes of transport.

Can you work out how many people fall into each category?

Solution:

Let:   C = people travel by ‘Car only’
T = people travel by ‘Train only’
B = people travel by ‘Bus only’
(C+T) = people travel by ‘Car & Train only’
(B+T) = people travel by ‘Bus & Train only’
(C+B) = people travel by ‘Car & Bus’’ only’
(C+B+T) = people travel by all three modes
P = total number that took part in the survey

Given:  

1. C = 2(C+T)
2. T = (B – 4)
3. (B+T) = 2(C+B+T)
4. (C+B) = B
5. C = (B+13)
6. (C+B+T) = 2
7. P = 62

Since,
         (C+B+T) = 2

Then
            (B+T) = 2(C+B+T) = 2*2 = 4

Adding the 7 survey parts of the Venn Diagram:

Number Sequence Puzzle

The 5th and the 9th terms in a regular number sequence are 11 and 17 respectively. What is the sum total of the first 20 terms in the sequence? Hint: Follow these 4 steps, which can be used for any normal sequences of numbers

1. Determine the values of the 1st and 20th numbers in the sequence.
2. Add the 1st and 20th terms together.
3. Divide Step 2 by 2, to find the average value of the number sequence.

Multiply Step 3 by the total number of terms in the sequence to get the total sum of the first 20 terms.

Solution:

Given: 5th term = 11, 9th term = 17 and total numbers in sequence = 20

1. The constant difference between terms = (17 – 11) / (9 – 5) or 6/4 = 1.5
   Therefore, the 1st term number = (5th term) – (4 x 1.5) = 11 – 6 = 5
   and the 20th term = 5 + (19 x 1.5) = 5 + 28.5 = 33.5
2. 5 + 33.5 = 38.5
3. 5 / 2 = 19.25
4. 25 * 20 = 385 (sum total of first 20 terms in sequence)

Tennis Match Puzzle

Margaret and Fiona decided to play tennis against each other. They bet £1 on each game they played. Margaret won three bets and Fiona won £5. How many games did they play?

Solution:

11.  Fiona lost three games to Margaret; she had lost £3 (£1 per game). She had to win back that £3 plus 3 more games, then win another 5 games to win £5 for a total of 11 games.