It's a bit of a trial/error approach, but it definitely works.
I think you hit on all the key concepts for the solution. It can be more elegantly summed up as:
Spoiler!
Start with an equilateral triangle of length 9.
Recognizing the internal angles are 120, and the complementary angles are therefore 60, it's a matter of chopping off 3 equilateral triangles off the original.
Quote:
Originally Posted by SebC
Spoiler!
I was going to go with no, but then I tested it (sort of cheating I guess) and I found one.
So here's how it works: for all interior angles to be equal, the interior angles must all be 120 degrees. So you have 6 across the top. Attach 1 on the left. Because that's a 60 degree triangle the width of the polygon added for that piece is 0.5. Stick the 2 on the right, horizontal distance added 1.0. Total 7.5. Connect the 5 to the one. 2.5 horizontal travelled. 4 to the 2. Width there is 2.0. Throw the 3 in the middle of the bottom, total horizontal of the bottom three segments is 7.5 again, so they match. Looking at the height of the polygon, you've got 5+1 on one side and 4+2 as the length of your slopes. Whether it is going left or right doesn't matter, the height scales with the total length so the heights of both sides are equal (height is 6*sqrt(3)/2=3*sqrt(3)).
Nice outside the box thinking, though not what I was expecting! The solution I'm looking for doesn't have non-standard renderings of the digits.
Spoiler!
So I'm guessing 19=11+8 rotating the observer's point of view 180 degrees isn't acceptable, then? (Since a standard 9 seems to have a line at the bottom).
So I'm guessing 19=11+8 rotating the observer's point of view 180 degrees isn't acceptable, then? (Since a standard 9 seems to have a line at the bottom).
Spoiler!
I think that's the right idea, with one small change: 19 - 11 = 8 is doable with the "standard" 9, moving a stick from the equal sign over to the minus sign to swap those symbols.
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I think that's the right idea, with one small change: 19 - 11 = 8 is doable with the "standard" 9, moving a stick from the equal sign over to the minus sign to swap those symbols.
I think full marks to Sebc as he got the "trick". Delayedreflex has the actual answer I was looking for.
Geez, I went and looked it up earlier, I don't like the solution at all. It says "move only 2 sticks to make a correct equation", it didn't say anything about also changing perspective, which would be doing more than moving 2 sticks. Heck, I could hold a piece of paper over match sticks I don't like, and "technically" be correct, too. Mine at least did exactly what the question said!
Geez, I went and looked it up earlier, I don't like the solution at all. It says "move only 2 sticks to make a correct equation", it didn't say anything about also changing perspective, which would be doing more than moving 2 sticks. Heck, I could hold a piece of paper over match sticks I don't like, and "technically" be correct, too. Mine at least did exactly what the question said!
It is a bit of a "bar" trick, to be sure, but I did say I accepted your solution. Be happy you came up with something original! Another possible unique solution is to change it to read 64=64 (if you don't care about spacing).
The puzzle reminded me of another matchstick problem:
Using 6 unbroken matchsticks of the same length, create 4 equilateral triangles.
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To do it on a surface, all you need to do is split the sticks into 3 groups of 2 sticks that are evenly spaced and parallel. Place one group horizontal, rotate one group 60 degrees clockwise and the other 60 degrees counter clockwise.
Once you've done that, you can position the three groups to overlap in many number of ways to form 4 triangles. Here's one way...
If there's no requirement that the triangles all be the same size, there are many different configurations that are possible.
In this diagram, if you moved the stick in the middle to the top, you'd have 6 total triangles, 2 large and 4 small (as it is, there are 5 if you count the large one).
If you move the triangles to create a Star of David, you can make 8 equilateral triangles... The two large ones and the six that form the points of the star.
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To do it on a surface, all you need to do is split the sticks into 3 groups of 2 sticks that are evenly spaced and parallel. Place one group horizontal, rotate one group 60 degrees clockwise and the other 60 degrees counter clockwise.
Once you've done that, you can position the three groups to overlap in many number of ways to form 4 triangles. Here's one way...
If there's no requirement that the triangles all be the same size, there are many different configurations that are possible.
In this diagram, if you moved the stick in the middle to the top, you'd have 6 total triangles, 2 large and 4 small (as it is, there are 5 if you count the large one).
If you move the triangles to create a Star of David, you can make 8 equilateral triangles... The two large ones and the six that form the points of the star.
SebC had the solution I remembered - maybe the original question required equilateral triangles the same length as the matchsticks?
I love your solution, getbak. In fact, in your diagram, you show 4 equilateral triangles of the same size, and a fifth that is larger. And, as you say, other configurations yield more like the star of David.
This puzzle was told to me by a friend this past week.
You have a 100kg object that is 99% water. You let some of the water evaporate from the object until the object is 98% water. How many kg is the object now?
This puzzle was told to me by a friend this past week.
You have a 100kg object that is 99% water. You let some of the water evaporate from the object until the object is 98% water. How many kg is the object now?
Spoiler!
So the object is 99kg of water. 99kg x 98%= 97.02kg(new mass) + 1kg(not water) = 98.02kg
Location: In my office, at the Ministry of Awesome!
Exp:
Spoiler!
When it’s 99% water and 100 kg that means you have 1 kg if non-water (let’s say salt)
After the water evaporates you still have 1 kg of salt that is now 2% of the mass (if the water is 98% the salt must me the remaining 2%.
We know the mass of salt so we can use that to figure out the mass of the total.
Total mass = 1 kg/0.2
Total mass = 50kg
1 kg salt
49 kg water
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Location: In my office, at the Ministry of Awesome!
Exp:
I’ll post one.
You have a 1 km track.
You are going to run 2 laps
You can run the first lap as fast or as slow as you want, call the speed on that lap Vone
You must run the second lap so that your average speed for the full 2km is twice as fast Vone.
i.e.
Speed lap 1 = Vone
Speed lap 2 = Vtwo
Average speed = Vave = 2*Vone
How fast do you have to run the second lap?
__________________
THE SHANTZ WILL RISE AGAIN. <-----Check the Badge bitches. You want some Awesome, you come to me!
When it’s 99% water and 100 kg that means you have 1 kg if non-water (let’s say salt)
After the water evaporates you still have 1 kg of salt that is now 2% of the mass (if the water is 98% the salt must me the remaining 2%.
We know the mass of salt so we can use that to figure out the mass of the total.
Total mass = 1 kg/0.2
Total mass = 50kg
1 kg salt
49 kg water
<-----Check the Badge bitches. You want some Awesome, you come to me!
