# Tag Archives: 3-digit Numbers

## 3-digit num3ers whose odd powers (1 to 19) end with the same num3er

This is the list of all 3 digit numbers, powers 1 to 19

## 4-digit number abcd = (k+a)(k+b)(k+c)(k+d)

abcd  =  (k + a)(k + b)(k + c)(k + d) abcd  is a 4-digit number and  k  is a positive integer.   For example, k = 5 1500  =  (5 + 1)(5 + 5)(5 + 0)(5 + … Continue reading

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## 3-digit Num3ers of the form x(x-y)+y(y-z)+z(z-x)=k, k=0,1,..,9

To find all 3-digit numbers   xyz   such that                  x(x – y)   +   y(y – z)   +   z(z – x)   =   k   k = 0 Solutions:    0,   111, … Continue reading

## 3-digit Num3ers w/ consecutive digits

123 + 132 + 213 + 231 + 312 + 321 = 1332 (123 + 132 + 213 + 231 + 312 + 321)/2 = 666 (123 + 132 + 213 + 231 + 312 + 321)/3 = 444 (123 … Continue reading

## Deleting the middle digit of 3-digit/5-digit numbers

(1) Let   N   be a 3-digit number (whose first digit is non-zero) and let   M   be the 2-digit number formed from   N   by deleting its middle digit                                      N   =   abc   … Continue reading

## Consecutive integers divisible by 3,5,7,9

Let’s look for consecutive numbers that are divisible by   3, 5, 7, 9   in that order (1) 3-digit numbers: 159   =   3 * 53                         … Continue reading

## Num3ers formed by its digits

132   =   13   +   31   +   12   +   32   +   21   +   23 123   =   132   –   (1 + 2^3) 312   =   … Continue reading

## 3-digit numbers ABC = k*(A + B + C)

To find all 3-digit numbers   abc   such that           100*a + 10*b + c   =   k*(a + b + c)   =   k*a + k*b + k*c   For example, k = 11 198   … Continue reading

## Products of 3-digit Num3ers are pandigital

For example, The 3-digit number   107   is multiplied by three different digits   3,   7,   8 107 * 3 = 321          107 * 7 = 749          107 * 8 = 856 The 3 products … Continue reading

## Concatenation puzzle: when (A || B) / B is an integer

Concatenation is the joining of two numbers by their numerals. That is, the concatenation of   444   and   777   is   444777. Concatenation of numbers   A   and   B   is denoted   A || … Continue reading

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