Question

I am thinking of a three digit number.It is an odd multiple of three,and the product of its digit is 24.It is larger than 15^2.what are all the numbers i could be thinking of

Answer 1

@e.mccormick

Answer 2

Well i found one
264 C:
Divisible by 3, product of its digits is 24, larger than 15^2

Answer 3

thats a odd multiple of 3

Answer 4

@e.mccormick

Answer 5

@phi

Answer 6

I only know one way to solve this, and that is by brute force search
if the 3 digits multiply to give 24, then they are factors of 24.
List all the factors of 24
1,24
2,12
3, 8
4,6

Now examine each pair
1 , 24 break 24 into its factors again), but only the 1 digit factos
1, 3, 8
1 , 4 ,6

to be divisible by 3, the digits must sum to a number divisible by 3
only 1,3,8 works (sums to 12)

now
2,12 --> 2, 1, 12
2, 2, 6
2, 3, 4
only 2,3,4 adds to a number divisible by 3

3, 8 -> 3, 1,8 repeat
3,2,4 repeat

4,6-> 4,1,6 not div by 3
4,2,3 repeat

I see only the combinations
1,3,8 and 2,3,4 (in any order)

we have these candidates
138 too small
183 too small
318 not odd multiple of 3
381 ****works
813 *** works
831 ***works
234 not odd mult of 3
243 **works
324 not odd mult of 3
342 not odd mult of 3
423 ***works
432 not odd mult of 3

I see 5 candidates: 243,381,423, 813, 831

Answer 7

oh thanks @phi

Answer 8

Awhs
I was wrong xc

Answer 9

to be absolutely sure, I would write a short computer program and double check. That is why people invented computers... to solve dumb problems like this one.