Puzzle 57
Imagine a chessboard of size 20 x 20 instead of the normal 8 x 8.
How many squares, of any size, are there in total?
workings
hint
answer
print
Share link – www.brainbashers.com/puzzle/zoiv
Hint
How many 1 x 1 squares are there, how many 2 x 2?
Answer
2,870 squares.
Reasoning
We have squares sizes from 1 x 1 up to 20 x 20, and these are the counts:
1 x 1 = 400
2 x 2 = 361
3 x 3 = 324
4 x 4 = 289
5 x 5 = 256
6 x 6 = 225
7 x 7 = 196
8 x 8 = 169
9 x 9 = 144
10 x 10 = 121
11 x 11 = 100
12 x 12 = 81
13 x 13 = 64
14 x 14 = 49
15 x 15 = 36
16 x 16 = 25
17 x 17 = 16
18 x 18 = 9
19 x 19 = 4
20 x 20 = 1
Total = 400 + 361 + 324 + 289 + 256 + 225 + 196 + 169 + 144 + 121 + 100 + 81 + 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 2870.
Puzzle 58
This BrainBashers safe has a rather unusual control panel.
In order to open the safe, you have to press every single square once only, in the correct sequence, ending on the square marked E.
Each square indicates which square to press next, for example, 2U means move up 2 squares and 3R means move right 3 squares.
Can you determine which square you must start with?
| 2R |
2R |
4D |
2D |
1R |
2D |
E |
| 2R |
1U |
3R |
2D |
1U |
4L |
3L |
| 1U |
1R |
4R |
2D |
1U |
2D |
2U |
| 3U |
5R |
2D |
3L |
1U |
3L |
2U |
| 2D |
2U |
2L |
2L |
1U |
2D |
1D |
| 3U |
2R |
1D |
2R |
1U |
2U |
6L |
| 6R |
3U |
2R |
2L |
1U |
2L |
2U |
Note: this puzzle isn't interactive, and the safe buttons can't be clicked.
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
Share link – www.brainbashers.com/puzzle/zcbs
Hint
Start anywhere and see where you end.
Answer
Start from the 2R on the sixth row down and the second column across.
Puzzle 59
Last week, I travelled from Birmingham to Glasgow (via bicycle).
On the first day, I travelled one quarter of the distance.
On day two, I travelled one half of the remaining distance.
On day three, I travelled three quarters of the remaining distance.
Yesterday I travelled one third of the remaining distance.
I now have 21 miles left to travel.
How far is it from Birmingham to Glasgow in total?
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
Share link – www.brainbashers.com/puzzle/zzva
Hint
How many miles were left at the start of yesterday?
Answer
336 miles.
Reasoning
To work these numbers out, it is perhaps easier to start at the end and work backwards.
Yesterday I travelled 1/3 of the distance to leave 21 miles, therefore there were 31.5 miles (=21 ÷ 2/3) at the start of yesterday.
On day 3 I travelled 3/4 of the distance to leave 31.5 miles, therefore there were 126 miles (=31.5 ÷ 1/4) at the start of day 3.
On day 2 I travelled 1/2 of the distance to leave 126 miles, therefore there were 252 miles (=126 ÷ 1/2) at the start of day 2.
On the first day, I travelled 1/4 of the distance to leave 252 miles, therefore there were 336 miles (=252 ÷ 3/4) at the start of the first day.
Double-Checking
On the first day, I travelled one quarter of the distance (84, leaving 252).
On day two, I travelled one half of the remaining distance (126, leaving 126).
On day three, I travelled three quarters of the remaining distance (94.5, leaving 31.5).
Yesterday I travelled one third of the remaining distance (10.5).
I now have 21 miles left to travel.
Puzzle 60
Can you find the country hidden in the following paragraph:
As a keen photographer, I find the best way to capture the portrait of a gazelle is to stand well downwind. I also try to wear clothes that blend in with the background to reduce the chances of scaring the animal.
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
Share link – www.brainbashers.com/puzzle/zayq
Hint
The country spans mode than one word.
Answer
India.
As a keen photographer, I find the best way to capture the portrait of a gazelle is to stand well downwIND. I Also try to wear clothes that blend in with the background to reduce the chances of scaring the animal.
< previous next >
Note: BrainBashers has a Dark Mode option – I recommend not using your browser's dark mode or extensions for BrainBashers
