It is so wonderful that there are such "theoretical questions" that make us think and reveal the ideas behind mysterious circuits.
When I read this question, my knee-jerk reaction was that this is impossible. But the problem remained dormant in my head, and at some point I began to make a connection with the somewhat strange circuit of an *amplifier with a T-bridge in the negative feedback*.
Basic idea
==========
... is extremely simple: According to Ohm's law, the current flowing through a resistor R with applied voltage V across it is I = V/R. If we actually supply the resistor with, for example, ten times lower voltage, the current will also decrease ten times (I = V/10R) and it will appear that the resistance has increased ten times (R = 10V/R).
Of course, there is a "small" catch here (as in any circus trick:-) - ***we see the voltage V when actually a voltage of V/10 is applied***.
Implementation
==============
Ohm's circuit with true 10 k resistance
-----------------
As an example, the current flowing through a 10 k resistor R with applied 10 V voltage V across it is I = 1 mA. We know that the resistance is 10 k but we can also measure the current and calculate the resistance - R = V/R = 10 V/1 mA = 10 k.
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[![STEP 1][1]][1]
Inverting amplifier with true 10 k R2
-----------------
As another example, the 10 k resistor R2 and R1 set a gain of -1 of an op-amp inverting amplifier.
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[![STEP 2][2]][2]
Ohm's circuit with virtual 100 k resistance
-----------------
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[![STEP 3_1][3]][3]
[![STEP 3_2][4]][4]
Inverting amplifier with virtual 100 k R2
-----------------
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[![STEP 4_1][5]][5]
[![STEP 4_2][6]][6]
Inverting amplifier with *T bridge* instead R2
-----------------
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[![STEP 5][7]][7]
[1]: https://i.sstatic.net/sBYk3.png
[2]: https://i.sstatic.net/S6sFy.png
[3]: https://i.sstatic.net/14vTT.png
[4]: https://i.sstatic.net/4k4QE.png
[5]: https://i.sstatic.net/xfiUA.png
[6]: https://i.sstatic.net/Y0kAG.png
[7]: https://i.sstatic.net/T07LS.png