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Every day, Little Johnny Red picks a positive integer $m$, arbitrarily permutes the digits of $m$ to a new integer $n$, and then computes the sum $m+n$. The sums that can be produced that way are called red integers.

Every day, Little Annie Yellow picks a positive integer $p$ that entirely consists of 1-digits$1$s, and then multiplies $p$ by nine. The products that can be produced that way are called yellow integers.

An integer is orange, if it simultaneoulsy belongs to the red and the yellow numbers.

Question: How many integers below one Googolplex are orange?

(Remark: All integers in this puzzle are represented in decimal, and all digits are decimal digits.)

Every day, Little Johnny Red picks a positive integer $m$, arbitrarily permutes the digits of $m$ to a new integer $n$, and then computes the sum $m+n$. The sums that can be produced that way are called red integers.

Every day, Little Annie Yellow picks a positive integer $p$ that entirely consists of 1-digits, and then multiplies $p$ by nine. The products that can be produced that way are called yellow integers.

An integer is orange, if it simultaneoulsy belongs to the red and the yellow numbers.

Question: How many integers below one Googolplex are orange?

(Remark: All integers in this puzzle are represented in decimal, and all digits are decimal digits.)

Every day, Little Johnny Red picks a positive integer $m$, arbitrarily permutes the digits of $m$ to a new integer $n$, and then computes the sum $m+n$. The sums that can be produced that way are called red integers.

Every day, Little Annie Yellow picks a positive integer $p$ that entirely consists of $1$s, and then multiplies $p$ by nine. The products that can be produced that way are called yellow integers.

An integer is orange, if it simultaneoulsy belongs to the red and the yellow numbers.

Question: How many integers below one Googolplex are orange?

(Remark: All integers in this puzzle are represented in decimal, and all digits are decimal digits.)

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Gamow
  • 45.9k
  • 10
  • 151
  • 387

Red, yellow and orange numbers

Every day, Little Johnny Red picks a positive integer $m$, arbitrarily permutes the digits of $m$ to a new integer $n$, and then computes the sum $m+n$. The sums that can be produced that way are called red integers.

Every day, Little Annie Yellow picks a positive integer $p$ that entirely consists of 1-digits, and then multiplies $p$ by nine. The products that can be produced that way are called yellow integers.

An integer is orange, if it simultaneoulsy belongs to the red and the yellow numbers.

Question: How many integers below one Googolplex are orange?

(Remark: All integers in this puzzle are represented in decimal, and all digits are decimal digits.)