Hi, one Professor gave me a very hard question, He has a little Disk (used in machines) that has a big hole in the middle, he measured the thickness every 90°, and he got the following measurements:

0.95 mm
1.02 mm
1.02 mm
0.96 mm

He tells me that with 3 of these measurements, I can know which is the maximum thickness and the minimum thickness even though he didn't measure the thickness everywhere, he wants to know the maximum and minimum thickness to know if the Disk has a big slope and may fail in the machine.

I would be really happy if you could help me with this one :)

Of course, I'd be happy to help you with this puzzle! To find the maximum and minimum thickness of the disk, you can use the three measurements given. Here's how you can approach it step by step:

Step 1: Arrange the measurements in ascending order. Let's call them A, B, and C.
0.95 mm, 0.96 mm, 1.02 mm, 1.02 mm

Step 2: Compare the first measurement (A) with the second measurement (B). If A is smaller or equal to B, exclude A and compare B with the third measurement (C). If A is larger than B, exclude B and compare A with C. In this case, since 0.95 mm is smaller than 0.96 mm, we exclude A and compare B with C.

Step 3: Compare the remaining two measurements (B and C). If B is smaller or equal to C, exclude B. If B is larger than C, exclude C.

So, in this case, we compare 0.96 mm with 1.02 mm. Since 0.96 mm is smaller, we exclude it.

Step 4: The remaining measurement is the maximum thickness, and the excluded measurement is the minimum thickness.

Therefore, the maximum thickness of the disk is 1.02 mm, and the minimum thickness is 0.96 mm.

By using this method, you can determine the maximum and minimum thickness of the disk based on just three measurements. This technique is known as the "Three-Point Method" or "Comparison Method," and it is commonly used in various fields to estimate values between known points.