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A really hard maths question. Try if you can

Umurbaba
in Applied Mathematics

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There is a 4 digit number which spells like "abcd". Jack, John and James tries to find this number. Jack only know the range of the digits(biggest -smallest).John only knows a+b+c+d.James knows a*b*c*d.

Jack says: I dont know all the digits but James doesn't either.

James says: I dont know all the digits but John doesnt either.

John says: I just found it and Jack should be just found it as well.

What is the four digits ?

However interesting, this isn't about a theorem or anything. Maybe it will get more attention if moved to Brain Teasers and Puzzles.

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