Question

I am a 4-digit number larger than 2,500. No two of my digits are the same. The product of the thousands digit and the hundreds digit is equal to the ones digit. The sum of my digit is 16.

Read the clues. Find the number

Answer 1

Explanation:

4-digit number abcd

a >= 2

a×b = d

so, 2 <= b <= 4 to allow a single digit result of a×b, and if b would be 1 or 0, the result would be either a copy of a or of b violating the rule that no 2 digits are the same.

that means a >= 3, because with a = 2 and b <= 4 the number can't be larger than 2500.

and that again means 2 <= b <= 3 and 3 <= a <= 4 to allow a single digit result of a×b.

the sum of "my digit" ? I guess you mean the sum of all digits is 16.

a + b + c + d = 16

so, my first guess :

a = 3

b = 2

therefore

d = 3×2 = 6

that means we have already 11 as sum of the digits, that leaves 5 for c.

so, the number would be

3256

the only alternative would start with a = 4 and then b = 2.

but that would make d = a×b = 8. abd 8 + 4 + 2 = 14, and that leaves for c only 2 to sum up to 16, and that would duplicate b.

so, 3256 is the only solution.