Sanjit sercet number

Number Theory Level 2

Sanjit gives the following hints about his secret number:

It a four digit number.
The product of the digits is 256.
The sum of the digits is 16.
It the same when read backwards.
It is more than 4000 and less than 5000.
It is even.

4334 There is no answer 5335 4444 4664 4994 4774 4554

1 solution

Maximos Stratis
Jun 3, 2017

Let's represent the number as: $abcd$ .
2. $a\times b\times c\times d=256$ .
3. $a+b+c+d=16$ .
4. $abcd=dcba$ .
From 4. we get: $a=d$ and $b=c$ .
From 3. we get: $2a+2b=16\Rightarrow a+b=8\Rightarrow a=8-b$ .
From 2. we get: $a^{2}\times b^{2}=256\Rightarrow a\times b=16\Rightarrow (8-b)\times b=16\Rightarrow b^{2}-8b+16=0\Rightarrow b=4$ .
So: $a=8-b\Rightarrow a=4$ .
Hence: $\boxed{abcd=4444}$ .

Sanjit sercet number

1 solution

0 pending reports