Puzzle 5
A large freshwater reservoir has two types of drainage system. Small pipes and large pipes.
6 large pipes, on their own, can drain the reservoir in 12 hours.
6 small pipes, on their own, can drain the reservoir in 18 hours.
How long will 6 large pipes and 6 small pipes take to drain the reservoir?
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
Share link: https://www.brainbashers.com/puzzle/znec
Hint
How many reservoirs can each drain in 36 hours?
Answer
7 hours and 12 minutes.
Reasoning
We can use a time that 12 hours and 18 hours both fit in to, in 36 hours:
6 large pipes can drain 3 reservoirs.
6 small pipes can drain 2 reservoirs.
Therefore, together, 6 large and 6 small pipes can drain 5 reservoirs.
36 hours ÷ 5 = 7.2 hours for one reservoir.
7.2 hours = 7 hours and 12 minutes for one reservoir.
Puzzle 6
In the following sum, the digits 0 to 9 have all been used, and the top row's digits add to 9.
Knowing that O = Odd, and E = Even (zero is even), can you determine each digit?
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
Share link: https://www.brainbashers.com/puzzle/zvzb
Hint
The answer is 4 digits long, so what must G equal?
Answer
423 + 675 = 1098.
Reasoning
Remembering that:
even + even = even
odd + odd = even
even + odd = odd
To discuss individual letters, it's easiest to represent the sum as:
A B C
D E F +
————————
G H I J
A + D has to be over 9, which means that G = 1.
B + E = I, is even + odd = odd, which means that we can't have a carry from C + F (otherwise it would have been even + odd + 1, which is even).
The 1 has already gone, so the smallest possible value for either C or F is 3, which means that the other can't be 7 or 9 (otherwise we'd have a carry).
Therefore, C and F are 3 and 5, but we don't know which is which. But we do now know that J = 8.
A + D = H, is even + even = even, which means that we can't have a carry from B + E. Therefore, E can't be 9, as this would force a carry. So E = 7.
I is the only remaining odd number, so I = 9.
Which means that B = 2.
Neither A nor D can be 0 (otherwise we would have two of the same digit). So, H = 0.
Therefore, A and D are 4 and 6 (but we don't yet know which is which).
Since the top row's digits have to add to 9, A can't be 6, so A = 4, making C = 3.
This makes the sum 423 + 675 = 1098.
Puzzle 7
My current age is the age of my favourite book (which is 14 years old) plus one third of my age.
How old will I be when my favourite book is twice its current age?
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
Share link: https://www.brainbashers.com/puzzle/znth
Hint
A little algebra might help.
Answer
I will be 35 in 14 years.
Reasoning
I am currently 21.
If X is my current age, then:
X = 14 + X
———
3
so
2X = 14
———
3
and
2X = 42
So
X = 21
I am currently 21 and my favourite book is currently 14 years old, when it is 28 years old (double its age) I will be 35.
Puzzle 8
Starting in the bottom left corner and moving either up or right, adding up the numbers along the way, what is the largest sum that can be made?
| 2 |
3 |
5 |
4 |
1 |
| 3 |
2 |
4 |
3 |
4 |
| 5 |
1 |
3 |
5 |
2 |
| 3 |
3 |
2 |
3 |
1 |
| 1 |
4 |
2 |
4 |
4 |
Note: this puzzle is not interactive, and the numbers cannot be clicked.
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
Share link: https://www.brainbashers.com/puzzle/zqio
Answer
The largest sum that can be made is 28.
< previous next >
Note: BrainBashers has a Dark Mode option. For BrainBashers, I'd recommend not using your browser's built-in dark mode, or any dark mode extensions (sometimes you can add an exception for a specific website).
