Alan

As follows:

Arun and Arjun are 2 shifty witnesses in a court case. Arun tells the truth 75% of the time, and Arjun tells the truth 80% of the time.

If they were to narrate the same incident, what is the percentage probability that they will contradict each other?

Prob = prob(Arun tells truth)*prob(Arjun lies) + prob(Arun lies)*prob(Arjun tells truth)

Prob = 0.75*0.2 + 0.25*0.8 = 0.35   or 35%

As follows:

The question might refer to cards with two digits, rather than cards with a number 2.

See https://web2.0calc.com/questions/help_21753

If you mean to do it in your head, then multiply 3456 by 100 and then subtract 3456.

If I've understood the question correctly (and I might well  not have!), it can be re-phrased as follows:

Assume I have two arbitrarily chosen integers, n and m.

Find another integer x such that for any integer, p, say, greater than or equal to x, that integer can be expressed as a sum of multiples of n and m.  i.e.  p = u*n + v*m,  where u and v are positive integers (or one of them is zero).

If my interpretation is correct, then

(a) if n and m are both even, there is no such x, since one can never find values of u and v such that u*n + v*m = p when p is an odd number.

(b) If one or both of n and m is/are odd, then I speculate that x = n*m  (but I've no proof, and I haven't tried hard to find a counter-example!).

mathmathj28 has the right values.

p(liquorice+mint) = (12/20)*(5/19)

p(liquorice+humbug) = (12/20)*(3/19)

p(mint+humbug) = (5/20)*(3/19)

sum the above to fiind the total probability:  (12*5 + 12*3 + 5*3)/(20*19)

I'll leave you to crunch the numbers.

Why don't you think that's correct?

Here's another way of doing it:

Clearly, 19 is the largest prime factor.