Meaning of "There's no saying" and "think up next"

[rich7]

Test No. incompl/elem-30 "Responses (3)", question 9

Mike: 'You just can't believe what they'll think up next, can you?'
Jane: '.........'

(a) There's no believing.
(b) There's no crediting.
(c) There's no saying.
(d) There's no announcing.

Test No. incompl/elem-30 "Responses (3)", answer 9

Mike: 'You just can't believe what they'll think up next, can you?'
Jane: 'There's no saying.'

Correct answer: (c) There's no saying.

Your answer was: incorrect
Mike: 'You just can't believe what they'll think up next, can you?'
Jane: 'There's no believing.'
_________________________

Dear Teachers,

Please explain both expressions.

Thnaks
rich7

[yo]

There's no saying means you are speechless and can't say anything to describe what is going on.

[blazya]

[Yankee]

[blazya]

Hi Yankee, your explanation was very good, indeed, thank you!! I don`d know what i`ll think up next, Do you? Is it OK?

[seanmen]

so, what does "that is no saying" actually mean?

did "yo" provide the right answer?
_________________
Hi, let's study English together.

[Yankee]

Hi

The idiom "there's no saying" means that 'it is not possible to anticipate or judge something' or simply 'it is not possible to say'.

I think yo's explanation fits the first test sentence (Mike). "You just can't believe what they'll think up next" means that whenever they think something up, it's hardly possible to believe what they've done or thought of doing. What they do is always so surprising/unexpected/unimaginable that you may well end up speechless.

Therefore, Jane's response is to agree that it's not possible to anticipate or imagine what they will do next: "There's no saying (what they will do next)."
.