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    How to work it out? I've no idea.

    The best thing to do is to just think of the voltmeters as 10MΩ resistors, as that's all they're doing in this situation. You can also treat R and V2 as a single resistor by using the formula for resistors in parallel Name:  resistance.png
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    If V1 has 4V, this means that the voltages are being shared in a 2:1 ratio between V1 and the R/V2 parallel bank. This means the ratio between their resistances must also be 2:1, so the total resistance of R and V2 must be half of the resistance of V1 (5V).

    This gets you  \frac{1}{5M\Omega} = \frac{1}{R} + \frac{1}{10M\Omega} which you can solve to get R=10MΩ
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