For a two digit number, the number on the single digit is 1 more than the square of the ten digit number. If you transpose the number on the single digit number with the ten digit number, the two digit number will be 27 larger than the original number Find the original two digits

For a two digit number, the number on the single digit is 1 more than the square of the ten digit number. If you transpose the number on the single digit number with the ten digit number, the two digit number will be 27 larger than the original number Find the original two digits

Let the original two digits be 10x + y
Then y = x ^ 2 + 1,10y + X - (10x + y) = 27
The solution is x = 2, y = 5
So the original number is 25

A two digit one digit number is one greater than a ten digit number. If you transpose a two digit number with a ten digit number, the product of the number you get and the original number will be zero
(1) A two digit one digit number is 1 larger than a ten digit number. If you transpose a two digit number with a ten digit number, then the product of the two digit number and the original two digit number is 108 larger than the square of the original two digit number. What is the original two digit number?
(2) Calculation; (2 + 1) (2 ^ 2 + 1) (2 ^ 4 + 1) (2 ^ 8 + 1) + 1
(3) Calculation; (2 ^ 2 + 2 ^ 4 +... + 100 ^ 2) - (2 ^ 2 + 3 ^ 2 +... + 99 ^ 2)

1) Let ten digits be x, then each digit is x + 1
The original number is 10x + X + 1 = 11x + 1
The transposed number is 10 (x + 1) + x = 11x + 10
From the meaning of the question, (11x + 1) * (11x + 10) = (11x + 1) ^ 2 + 108
Just solve the equation
2) Original formula = [(2-1) (2 + 1) (2 ^ 2 + 1) (2 ^ 4 + 1) (2 ^ 8 + 1)] / (2-1) + 1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)+1
=(2^4-1)(2^4+1)(2^8+1)+1
=(2^8-1)(2^8+1)+1
=(2^16-1)+1
=2^16
3) Is your question (2 ^ 2 + 4 ^ 2 +... + 100 ^ 2) - (1 ^ 2 + 3 ^ 2 +... + 99 ^ 2)
Open the brackets and use the square difference formula
=2^2-1^2+4^2-3^2+.100^2-99^2
=(2-1)(2+1)+(4-3)(4+3)+.(100-99)(100+99)
=3+7+11+.+199
=5050

There is a three digit number. The sum of the three digits is 16. The ten digit number is the sum of the one digit number and the one hundred digit number. If the one hundred digit number and the one hundred digit number are exchanged
Then the new number is 594 larger than the original number, and the original number can be found

If the individual digit is x and the hundred digit is y, then the ten digit is x + y
From the meaning of the title: x + y + X + y = 16, x + y = 8 (1)
100Y+10(X+Y)+X+594=100X+10(X+Y)+Y
99(X-Y)=594
X-Y=6 (2)
(1) + (2) get 2x = 14, x = 7
So y = 1
So x + y = 8
So the original number is 187