Puzzle 13
During a recent BrainBashers race meeting, the fastest driver managed to complete a lap with an average speed of 150 mph.
They managed to complete the first two fifths of the lap at a speed of 123 mph and the second two fifths of the lap at a speed of 164 mph.
At what speed was the final one fifth of the lap length covered?
The answer is not 176 mph.
Puzzle Copyright © Kevin Stone
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Hint
Adding the speeds won't work.
Answer
205 mph.
Reasoning
If we take the number of miles in a lap to be L miles and use Time = Distance ÷ Speed.
The first 2/5 are covered at 123 mph. Therefore, the time taken was [(2/5) x L] ÷ 123 hours.
The next 2/5 are covered at 164 mph. Therefore, the time taken was [(2/5) x L] ÷ 164 hours.
The last 1/5 is covered at y mph. Therefore, the time taken was [(1/5) x L] ÷ y hours.
The entire trip is covered at an average of 150 mph, and we can conclude that:
2L 2L L L
————— + ————— + ——— = ———
5x123 5x164 5y 150
Rearranging and simplifying gives:
1 1 2 2
——— = —— - ——— - ———
y 30 123 164
That means that y = 1 ÷ (1/30 − 2/123 − 2/164)
Using a calculator gives y = 205.
Puzzle 14
Moving from letter to letter using the moves of a chess knight, can you find the letters 'PUZZLES' in order?
| Z |
E |
Z |
S |
Z |
P |
S |
| U |
P |
S |
P |
L |
P |
Z |
| S |
U |
L |
U |
U |
E |
U |
| E |
E |
P |
U |
S |
U |
P |
| P |
Z |
L |
L |
U |
P |
Z |
| Z |
U |
Z |
S |
U |
L |
P |
| E |
P |
Z |
Z |
E |
L |
U |
Note: this puzzle is not interactive, and the squares cannot be clicked.
The moves of a knight are:
Puzzle Copyright © Kevin Stone
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Hint
It might be easier to find the S first.
Answer
Start with the P in the 5th row, 6th column:
Puzzle 15
What number comes next in this sequence:
1 · 23 · 124 · 1251 · 26127 · 128129 · ?
Puzzle Copyright © Kevin Stone
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Hint
Try removing the spaces from the sequence.
Answer
1301311 or 1210121.
Reasoning
Removing spaces from the original sequence gives:
1 23 124 1251 26127 128129
123124125126127128129
Now adding spaces back in, in the correct place:
123 124 125 126 127 128 129
The next few terms could be:
130 131 132
or
1210 1211 1212
Add these to the end:
123 124 125 126 127 128 129 130 131 132
or
123 124 125 126 127 128 129 1210 1211 1212
Remove the spaces again:
123124125126127128129130131132
or
123124125126127128129121012111212
Now break the sequence into chunks of increasing size:
1 23 124 1251 26127 128129 1301311
or
1 23 124 1251 26127 128129 1210121
So the missing term is 1301311 or 1210121.
Puzzle 16
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?
| 6D |
2D |
3R |
1R |
2D |
1D |
6L |
| 2R |
1U |
2R |
2L |
2D |
2D |
2D |
| 1U |
1D |
2U |
1U |
1L |
3L |
1U |
| 2D |
1L |
2D |
3U |
2D |
2L |
4L |
| 2U |
1R |
2R |
3R |
E |
2U |
5L |
| 3R |
1D |
4R |
1U |
3L |
1U |
1D |
| 2U |
1R |
1R |
1R |
1R |
1U |
6U |
Note: this puzzle is not interactive, and the safe buttons cannot be clicked.
Puzzle Copyright © Kevin Stone
workings
hint
answer
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Hint
Start on any square, and see how far you can get.
Answer
Start from the 1U that is on the 3rd row down and the 7th column across.
