That is strange!
- Do you like my three digit number?
- Not too bad, but look at this!
- What?
- When I multiply the three digits the result is 1/5 of the original number.
- That is strange!
- I agree. I thought it would be bigger.
- Do you like my three digit number?
- Not too bad, but look at this!
- What?
- When I multiply the three digits the result is 1/5 of the original number.
- That is strange!
- I agree. I thought it would be bigger.
June 29th, 2009 at 3:25 am
Let the number be n and the product of n’s digits be p.
p = n/5, so n is a multiple of 5. If n ended in 0, p would be 0, leading to the trivial solution n=000.
Otherwise, n ends in 5. Thus p is a multiple of 5, so n is a multiple of 25, thus ends in 25 or 75. It’s then a simple matter of checking cases to find n=175, p=35.
Alternatively: n=25k for some odd k, so p=5k, so p is odd, so all n’s digits are odd, so n ends not in 25 but in 75. Then check cases.