Digit 2 is smaller than Digit 4Digit 4 is two thirds of Digit 1Digit 1 is two thirds of Digit 3Digit 3 is three times Digit 2
By (3), Digit 3 is divisible by 3:
Digit 3 = 3, 6, 9
By (3), Digit 1 is two thirds of Digit 3:
Digit 1 = 2, 4, 6.
But, by (2), Digit 1 is divisible by 3:
Digit 1 = 6, and Digit 3 = 9.
By (4), Digit 3 is three times Digit 2:
Digit 2 = 3.
By (2), Digit 4 is two thirds of Digit 1:
Digit 4 = 4.
??
Puzzle 42
Can you find the number that best completes this puzzle?
The middle of each triangle contains the square root of the sum of the three surrounding numbers.
??
Puzzle 43
During the recent BrainBashers Football Competition, 5 teams were competing.
Each team played each other just once, with 2 points for a win, 1 point for a draw, and 0 points for a loss.
However, the rain damaged the final scoresheet, and this is all that could be read of the final points after all of the matches:
Rugby 6
Grimsby 5
Hereford 4
Lichfield 2
Reading {?}
Can you work out how many points Reading ended the season with?
Reasoning
There were 5 teams in the league, and every team played every other, so there were a total of 10 games played:
Rugby vs Grimsby
Rugby vs Hereford
Rugby vs Lichfield
Rugby vs Reading
Grimsby vs Hereford
Grimsby vs Lichfield
Grimsby vs Reading
Hereford vs Lichfield
Hereford vs Reading
Lichfield vs Reading
We know that 2 points were allocated for each game played. Which means that there were a total of 20 points over the 10 games.
Since the given results add to 17, the remaining 3 points belong to Reading.
?
Puzzle 44
Last week, I travelled from London to Stoke.
On the first day, I travelled one half of the distance.
On day two, I travelled one third of the remaining distance.
On day three, I travelled three quarters of the remaining distance.
Yesterday I travelled one half of the remaining distance.
Reasoning
I now have 5 miles left to travel, so I must have travelled 5 miles yesterday.
At the end of Day 3, I had 10 miles left to travel, so I must have had 40 miles left at the start of the Day 3.
At the end of Day 2, I had 40 miles left to travel, so I must have had 60 miles left at the start of the Day 2.
At the end of Day 1, I had 60 miles left to travel, so I must have had 120 miles left at the start of the Day 1.
Double-Checking
On the Day 1, I travelled 60 miles, leaving 60 miles.
On Day 2, I travelled 20 miles, leaving 40 miles.
On Day 3, I travelled 30 miles, leaving 10 miles.
Yesterday, I travelled 5 miles, leaving 5 miles.
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).
