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.

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

@Zakir Husain, @Pi Han Goh, @Vinayak Srivastava, @Mahdi Raza, @Aryan Sanghi

Yajat Shamji - 11 months, 1 week ago

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

Zakir Husain - 11 months, 1 week 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

Mahdi Raza - 11 months, 1 week ago

@Gandoff Tan

Yajat Shamji - 11 months, 1 week 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 $x=1729$

Zakir Husain - 11 months, 1 week ago

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

There might be infinite of these

Mahdi Raza - 11 months, 1 week ago

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

Zakir Husain - 11 months, 1 week ago

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

Mahdi Raza - 11 months, 1 week ago

@Mahdi Raza – thanks!

Zakir Husain - 11 months, 1 week ago

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

Yajat Shamji - 11 months, 1 week ago

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

Yajat Shamji - 11 months, 1 week ago

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

Yajat Shamji - 11 months, 1 week ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Number Spy Challenge 111

Comments

Number Spy Challenge $1$