#### Problem. Find a four digit number

Find a four digit number, knowing that their sum is 23 , the product of the first two digits is 24 , the sum of the first three digits is 19 and the sum of the first and last digit is 10

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### Exemple !

Find a four digit number, knowing that their sum is 20, the product of the first two digits is 15, the sum of the first three digits is 25 and the sum of the first and last digit is 8.

We note: with a - the first digit, b - the second digit, c - the third digit, d - the fourth digit

Because

a + b + c + d = 20

a + b + c =15

We will calculate the fourth digit which is equal to the difference of the two sums

d = 20 - 15

d = 5

Knowing that the sum of the first and the last digit is 8

a + d = 8

a + 5 = 8

a = 3

and that the product of the first two digits is 15

a * b = 15

a = 3

3 * b = 15

b = 5

We calculate the third digit by subtracting from the given sum the two known digits.

c = 15 - b - a

c = 15 - 5 - 3

c = 7

We will write the number

abcb

3575

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