There are several Shrine Locations in The Legend of Zelda: Tears of the Kingdom that help you test out your in-game skills with unique puzzles and challenges.
The Eutoum Shrine puzzle in Zelda: Tears of the Kingdom is actually a Proving Grounds shrine that features a mixture of combat and stealth. You’ll be stripped of your regular equipment upon entry and will have to learn to make do with standard wooden gear and improve it as you go.
Here’s how you complete the Eutoum Shrine Proving Grounds puzzle in Zelda: TotK.
Where to find the Eutoum Shrine in Zelda: TotK

Coordinates: -3506, 3570, 038
To approach the Eutoum Shrine your best starting location should be the Rospro Pass Skyview Tower in Tears of the Kingdom.
You can head to this tower and use the sky launch here to see the shrine location to your north. From there you can glide in that direction to reach the shrine’s coordinates.
You can find the shrine by heading toward the northern end of the Hebra region in TotK. You can confirm that you are on the right path once you find yourself in a mountainous area and see Goflam’s Secret Hot Springs.
How to complete the Eutoum Shrine in Zelda: TotK
Tackling this Proving Grounds: Infiltration challenge at the Eutoum Shrine in Tears of the Kingdom will be heavily reliant on the effective usage of your Fuse ability.
As soon as you’ll enter the shrine all your gear will be removed and you’ll be given an Old Wooden Shield, Long Stick, and Wooden Stick in exchange. Look to your left at the shrine entrance and you can grab them from there.

You’ll have to take out 5 Constructs to pass this challenge. The first one will be to your right. You can either sneak up to kill it or charge straight forward. For a stealthy approach head straight and circle all the way around toward it and take it out by pressing Y to execute a Sneak Attack.
After you kill the first Construct, it will drop its Zonai Charge. Now, use your Furse ability and combine it with your Wooden Stick.
You’ll also need to increase your attack range to avoid getting hit by the other Constructs. So, try combining your Wooden Long Stick with its Construct Horn using Fuse.
Now turn the corner to find another construct. Here you can take advantage of your new increased-range Long Stick to take out the construct.
It will now drop a bow that will be especially useful for increasing your range. You’ll also have a limited number of arrows, so keep that in mind. You’ll also need to remove the spike traps blocking your path.
To do so use your Fuse ability once more and this time combine them with your shield. The other Construct uses a Shock Emitter Bat. it must be killed next since it drops a Soldier Construct II Horn. You’ll need it to improve your Long Stick again.

Remember, that since these two Constructs are close together, you’ll need to separate them to avoid getting sandwiched. Keep your distance using your Long Stick.
Now there are two Constructs remaining, one with a Spiked-Iron-Ball Hammer and the other with Shock Fruit lightning arrows. Bait the hammer one toward you and strike them down.
The second one will prove trickier. You’ll have to keep your distance and use the bow you picked to chip away at them. You can throw your other weapons as well if your arrows run out.
After all 5 Construct have been dealt with the Proving Grounds: Infiltration challenge will be completed and the Shrine door will open. You’ll also receive a Sapphire and Light of Blessing after you open the chest.