# Tag Archives: 3-digit Numbers

## 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

## 3-digit Num3ers N=abc, f(N)=a+b+c+a*b+a*c+b*c+a*b*c

N   =   abc, f(N)   =   a   +   b   +   c   +   a*b   +   a*c   +   b*c   +   a*b*c Can you find a 3-digit number … Continue reading

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## 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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## A 3-digit num3er divisible by 7

Let   abc   be 3-digit number.   abc   is divisible by 7. Prove that 7 can be cancelled out of the fraction             bc   +   16*a           ——————–           bc   –   61*a   … Continue reading