# Number Spy Challenge $1$

Find a number that when divided by the Hardy-Ramanujan taxicab number $1$, it produces a number such that the sum of it's digits is equivalent to a quarter of a power of $2$.

In simplified terms:

$\frac{x}{1729}$ $= abcd$ such that $a + b + c + d =$$\frac{2^n}{4}$

The only condition is that $x \geq 1729$ as $\frac{1729}{1729}$ $= 1$.

You're looking for the first number.

Note by Yajat Shamji
4 months, 3 weeks ago

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Sort by:

- 4 months, 3 weeks ago

@Yajat Shamji- Is $abcd=a\times b\times c \times d$ or they are digits?

- 4 months, 3 weeks ago

I think $abcd$ is the four-digit number. Yes, I agree that it might be confusing because the result can be more than a four-digit number, but let him clarify

- 4 months, 3 weeks ago

- 4 months, 3 weeks ago

As $x$ can be equal to $1729$ ($\because x\geq1729$). If $x=1729$ then $a=0,b=0,c=0,d=1;a+b+c+d=1=\dfrac{2^2}{4}$ therefore $x=1729$

- 4 months, 3 weeks ago

$\dfrac{1729}{1729} = 0001 = 0 + 0 + 0 + 1 = 1 = \dfrac{2^2}{4}$

There might be infinite of these

- 4 months, 3 weeks ago

It is written that $\dfrac{x}{1729}=abcd;a+b+c+d=\dfrac{2^n}{4}$ not $\red{\dfrac{x}{1729}=\dfrac{2^n}{4}}$

- 4 months, 3 weeks ago

What is asked is the sum of digits after the division and that is 1

- 4 months, 3 weeks ago

thanks!

- 4 months, 3 weeks ago

No. What is asked is that the sum of the digits equals a quarter of a power of $2$.

- 4 months, 3 weeks ago

Thanks for finding the first number, @Mahdi Raza, @Zakir Husain!

- 4 months, 3 weeks ago

@Mahdi Raza, @Zakir Husain - I am posting Number Spy Challenge $2$ in $\leq 5$ minutes! After that, I'll see you tomorrow!

- 4 months, 3 weeks ago