亿博体育 Brainteaser: April
28 Apr 2025
Each month, 亿博体育 sets a weekly brainteaser, with questions of varying degrees of difficulty. Readers supplying the most accurate (and stylish) answers are then considered for the prestigious Brainiac of the Month title.
Question 4: Security check
Sean has secured his suitcase with two combination locks, each having a five-digit code. For the codes, he decided to use the smallest and largest numbers that met the following conditions:
Each digit of the number was a prime digit,
Each successive pair of digits formed a two-digit number that was not a prime number,
Each of the prime digits had to appear at least once in the five-digit number.
What were the codes for Sean’s combination locks?
Email your answer: correct replies on Friday.
Question 3: Tree fellers
If it takes Tim 1 hour and 40 minutes to fell a tree, how long will the same job take if he is joined by Terry and Tom working respectively 10% and 20% faster?
Answer: A select group of our top Brainiacs made short work (see Solutions) of this EUDR-compliant question: Well done to: Bharat B Sharma, technical director, TWC Group (Rajsha Chemicals Pvt. Ltd), Vadodara (Guj) India; John Bowen, consultant, Bromsgrove, UK; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; and everyone else who had a go.
SOLUTIONS
Bharat B Sharma
Let’s say, the speed of cutting tree (Choppinmg speed) of Tim is x/minute
Total chopping required in1hour40 Minutes (time taken by Tim is 100 minutes) = 100 xChoppings.
Chopping Speed of Terry = 1.1x/minute (10% faster than Tim)
Chopping Speed of Tom = 1.2x/minute (20% faster than Tim)
If all three work together, the total speed will be x+1.1x+1.2x = 3.3x/minute
Total time that will be required = 100x / 3.3x minutes = 100/3.3 minutes = 30.303 minutes!
Answer- 30.303 Minutes
John Bowen
Let Tim's work rate = 1.0, so to fell a tree takes 100 man minutes.
Total work rate when all 3 are working together = 3.3, so time to do 100 man minutes of work is now 100/3.3 minutes
= 30.30 minutes or 3minutes 18 seconds
Kamila Staszewska
Tim cuts 1 tree in 1h40min=100min; 1/100=0.01 tree/min
Terry: +10% = 1.1 tree per 100min=0.011 tree/min
Tom: +20% = 1.2 tree per 100min=0.012 tree/min
Workers combined = (1+1.1+1.2)/100= 3.3/100=0.033 tree/min
0.033 tree - 1 min
1 tree - x min
x= 1/0.033=30.3min=30min18s
Sudi Sudarshan
Solution:
Tim's speed of felling a tree = 1/100 trees per minute
Terry's speed of felling a tree = (1/100)*1.1
Tom's speed of felling a tree = (1/100)*1.2
Combined speed of the three men for felling a tree = (1/100)+ (1/100)*1.1 + (1/100)*1.2 = (1/100)* (1+1.1+1.2) = 3.3/100 trees per minute
Time taken by the three men working together to fell a tree = 1/(3.3/100) = 100/3.3 = 30.3030...
So, it takes 30.30 minutes for the three men together to fell a tree.
Amparo Botella
The time to cut 1 tree is 30 minutes and 18 seconds.
Tim takes 1 hour and 40 minutes, which is 100 minutes, to fell a tree.
So his work rate is 1 tree100 minutes=0.01 trees/minute
Terry is 10% faster than Tim, so his rate=0.01×1.10=0.011 trees/minute
Add all their rates together:
Total rate=0.01+0.011+0.012=0.033 trees/minute
if in 1 min. we cut 0.033 trees then 1 tree will be cut in: 1/0.033= 30.3 minutes
That’s approximately 30 minutes and 18 seconds.
New teaser on Monday
Question 2: Easy rider
On his regular 2km commute, Barry took three minutes to cycle to work with the wind directly behind him, and returned home in four minutes, cycling against the same wind-force. How long would his total commuting time have been if there was no wind?
Answer: This week, the yellow jerseys (see Solutions below) go to: John Bowen, consultant, Bromsgrove, UK; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Bharat B Sharma, technical director, Rajsha Chemicals Pvt. Ltd, (TWC Group), Vadodara (Guj) India; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; Alfred Johnson, AlMailem Tires, Kuwait. Well done to everyone else who had a go.
SOLUTIONS
John Bowen
We need to use the basic equation of motion and set up 2 simultaneous equations and assume that the effects of the wind, when blowing, are equal and opposite in effect..
Into work, distance is 2km, time taken is 3 minutes with wid behind, so let cycling speed = V, wind speed effect = W, so
[V + W] =2/0.05 = 40km/hr [Velocity = Distance/Time
And after work, time taken is 4 minutes against the wind
[V - W] =2/0.066666 = 30 km/hr
Adding these 2 equations, 2V = 70, so V = 35km/hr.
So, his total commuting time in the absence of wind = Distance/Time = 4km/35km/hr = 0.11426hours or 6,857minutes or 6minutes51.4seconds
Kamila Staszewska
To work, with wind: 2 km in 3 min (0.05h), Speed= 2/0.05=40km/h (v+ w); v – Barry’s speed and w - wind,
To home, against wind: 2km in 4 min (0.0666h), Speed=2/0.0666=30km/h (v – w)
Barry’s speed without wind: (v+w)+(v-w)=2v=40+30; v=35km/h
Time of travel both ways without wind = 4km / 35km/h = 0.114h=6min51s
Sudi Sudarshan
Let S be the speed of the bike without wind and W the wind speed.
On the trip to school, relative speed is S+W
S+W = Distance/Time = 2 / 3 Km per second
On the return trip, relative speed is S-W
S-W = Distance/Time = 2/4 = 1/2 Km per Minute
Adding the two equations:
2S = 2/3 + 1/2 = 7/6
S = 7/12 Km per Minute
Total distance for the roundtrip = 4 Km
Time for the entire commute without wind = Distance/Speed = 4/(7/12) = 48/7 = 6.86 Minutes or 6 minutes 51.4 seconds
Bharat B Sharma
Say Cycling speed is xmet/min
and wind speed is y met/min
With wind in favour 3x+3y=2000
12x+12y=8000
(#1) Multiplying by 4
With wind against 4x-4y=2000
12x-12y=6000
(#2)... Multiplying by 3
Adding both equation #1 
24X= 14000
Speed x = 14000/24 =
583.3333333
m/min
Total distance for return trip = 4000m (2 km each way)
With no air speed, the time required will be distance/speed
6.857142857 minutes.
Amparo Botella
The time to get home with no wind will be 3,428 minutes.
V= speed with no wind (km/min)
W=speed with wind (km/min)
With wind: V+W=2/3Without wind: V-W=1/2
Then:
(V+W)+(V´W) = 2/3+1/2
2V=7/6
V=7/12 km/min.
To calculate the time to make 2 km.:
Time = 2/V = 2/(7/12) = 24/7 minutes = 3,428 min.
Alfred Johnson
C = Cycling Speed without wind
W = Wind Speed
Distance / Time = Speed
2 Km / 3 Min = C + W
2 Km / 4 Min = C - W
======================
0.666 + 0.50 = C + W + C - W
C = 0.583 Km / Min
Answer : Barry could have taken 4 Km / 0.583 = 6.861 Min = 6 Min 51 Sec to complete the trip without wind, instead of 7 Mins.
0.5 Km / Min! That's quite fast! :)
Please note: Due to the UK Easter holidays the next teaser will be issued Tuesday 22 April.
Question 1: Make my day
2nd of May
7th of September
4th of March
?
Answer: As easy as ABC(D) once you saw the connection... but also a couple of great alternative answers (see Solutions). Very well done: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Jim Cristiano, director, category management, Veritas + HDT Automotive Solutions LLC, world headquarters, Livonia, Michigan, USA; Hans-Bernd Luechtefeld, consultant, Germany; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Ian Brooker, Sr. buyer, HB Chemical Corp., a Ravago company, Twinsburg, Ohio, USA; David Mann, Polymer Business Development consultant, UK; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain.
SOLUTIONS
Andrew Knox
Answer: 1st of December (a, b, c, d,...).
Hans-Bernd Luechtefeld
1st of December,
According to the following logic:
2nd letter in May is 'A', 7th in September is 'B' and 3rd in March is 'C'. Now, looking for a Month with 'D', following the alphabetical order is December only, with the first letter.
Jim Cristiano
2nd of May - 2nd letter is A
7th of September - 7th letter is B
4th of March - 4th letter is C
1st of December - 1st letter is D
Sudi Sudarshan
Solution: Each entry refers to the position of a letter in the word representing a month.
2nd of March refers to the letter a
7th of September refers to the letter b
4th of March refers to the letter c
In the order, the next letter of the alphabet is d.
December is the only month with the letter d, and it is the first letter of the word.
So 1st of December is the letter d
David Mann
If the pattern is 2nd letter of May (A) etc then the sequence is ABCD
The next one can only be 1st of December.
ALTERNATIVELY
Amparo Botella
If we follow the pattern that 2+2=4, 7+2=9 so the day could be 9th.
The same with the month, May (5) – March (3) = 2 so September (9) – 2 = 7 July.
Kamila Staszewska
The pattern is the following: the date is 7th of November