How do you create a cell to type in any numbers to test for Armstrong Numbers up to 6 digits and a corresponding cell to automatically display yes or no?

Answer 1

Armstrong numbers are the sum of their own digits to the power of the number of digits. Here are all the possible Armstrong Numbers up to six digits:

1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, 548834

EXAMPLE: 153 = 13 + 53 + 33

Sometimes, the simple solutions are better than complicated elegant solutions. Just compare your number to the list. If your number is on the list, it is an Armstrong Number.

Designing a spreadsheet formula to compare all numbers 1-6 digits to determine if they are one of twenty possible numbers does not make sence. However, in the spirit of education (even though using this solution does not pass the common sense test), here are two methods you can use to solve this problem.

SOLUTION #1 (easy): Compare against a look-up table.

=IF(ISERROR(VLOOKUP(A1,C1:C20,1,FALSE)),"No","Yes")

1. Reserve A1 for entry of the number to be evaulated.
2. In B1, enter this formula: =IF(ISERROR(VLOOKUP(A1,C1:C20,1,FALSE)),"No","Yes")
3. In column C (C1:C20), enter the first twenty Armstrong Numbers [see list above].
4. Enter a number in A1 and observe "Yes" or "No" in B1.

SOLUTION #2 (difficult): Brute force calculation.

=IF(LEN(F1)=6,IF(MID(F1,1,1)^6+MID(F1,2,1)^6+MID(F1,3,1)^6+MID(F1,4,1)^6+MID(F1,5,1)^6+MID(F1,6,1)^6=F1,"Yes","No"),"Not 6 places")

Here is an example for 6-digit numbers (use the same procedure for other size numbers or write a macro that will count the characters and loop through as many times as necessary):

1. Reserve A1 for entry of the number to be evaulated.
2. In B1, enter this formula:

   =IF(LEN(F1)=6,IF(MID(F1,1,1)^6+MID(F1,2,1)^6+MID(F1,3,1)^6+MID(F1,4,1)^6+MID(F1,5,1)^6+MID(F1,6,1)^6=F1,"Yes","No"),"Not 6 places")

3. In B1, observe "Yes" or "No" (if you have not entered a 6-digit number, you will see "Not 6 places.")