We love math and logic puzzles, which is why we regularly recruit the world’s sharpest minds to come up with riddles that test your critical thinking, math, and logical skills. The next riddle is an especially tiring problem, so grab a pencil and a piece of scratch paper and get ready to tear your hair out (in the best way). Oh, and of course, no cheating.
➡ The problem
The fearsome Sheriff of Nottingham plans to gather his troops in his fortress, protected by a large moat with a single drawbridge. As the drawbridge begins to rise behind the sheriff’s troops, a lone figure appears in the field before the castle: the one and only Robin Hood!
The legendary archer’s only chance to save the people of Sherwood Forest is to race into the fortress on his trusty steed, jump the bridge before it closes, and disrupt the meeting before it can begin. With his incredible tactical acumen, Robin Hood surveys the terrain and begins to lay out a plan.
The drawbridge is 9.7 meters long (32 ft). It is already raised 0.6 meters from the ground (2 feet) and appears to be rising at a constant rate of 2 degrees per second. Robin Hood is 200 feet (61 meters) from the edge of the drawbridge. Without hesitation, he spurs his horse into a gallop and tries to jump before it’s too late.
So how does this story end? Does Robin Hood make it to the bridge? Or does he end up getting himself out of the pit?
➡ The track
This problem requires you to make some assumptions. The first must be that a drawbridge at rest is flat against the ground. Don’t worry about uneven terrain.
➡ The solution
Ready for the solution? Well here you have it. Again, don’t cheat…
This problem requires us to compare two things: the physical ability of Robin Hood’s horse and the height of the bridge over time. One of them requires an estimate, while the other can be calculated directly.
Like any creature, horses that are trained to jump develop muscles that allow them to jump much better than their peers. Typical show horses start jumping over 2.5 to 3 feet (0.7 to 0.9 meters) hurdles, with a world record of just over 8 feet (2.4 meters)
As for the gallop speed, the average horse reaches between 40 and 48 Kph, that is, approximately 12 meters per second (40 feet per second). Suppose the horse can gallop and jump without significantly changing speed. That means an average horse will cross the 200-foot course to the bridge in 5 seconds.
So our new task is to find out the height of the bridge after 5 seconds. We know that it starts at 0.6 meters (2 feet) and that the angle that the far side of the drawbridge makes with the ground increases at 2 degrees per second. After 5 seconds, we have added 10 degrees. What angle did you start with? Let’s make a sketch.
Let’s call the angle a. When we pose this problem with a right triangle, we see that the easiest path to a solution involves some basic trigonometry. The sine ratio compares an angle to the opposite side divided by the hypotenuse.
Thus, a horse galloping at an average speed would need almost a world record jump to reach the bridge and the castle. But didn’t we say that Robin Hood probably had a faster horse? Let’s consider three mounts: the Leaper, the Cannon, and the Faithful Steed.
Jumping is not impossible, but you do need a trained horse that is above average in terms of speed and jumping ability. Our trusty steed came the closest, and will indeed jump the jump if he runs a little faster: 19.3 meters/sec (63.3 feet per second). or about 69.5 kph. A small but significant raise for the likes of the legendary Robin Hood.
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Can you solve the Robin Hood riddle?
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