Four positive numbers
Four positive integers which are different from each other total less than 18. To find out the four numbers you need to know their product and the smallest number.
But you don't know their product and you don't know the smallest number . . . or do you?
But you don't know their product and you don't know the smallest number . . . or do you?
Labels: logic, mathemagic
posted by Rajesh Lal at
9:39 AM
15 Comments:
That doesn't make much sense. If you don't want to talk about it/ post a suggestion/ find the answer, don't click on post reply.
Assuming that
"positive integers which are different from each other"
refer to Primary numbers.
the four numbers are 2, 3, 5, 7.
well
then numbers are 1,2,3 and 4
their total is 10, product is 24
10 is smaller than 18
24 doesnt need to be smaller than 10
they are all positive numbers and they are all different
so... i think this fits the criteria
Am I missing something on this one. 1 2 3 4. These are four positive integers that total 10, less than 18, and they are different from each other.
Other variations that work are:
1 2 3 5
1 2 3 6
1 2 3 7
and so on.
I don't get the point on this one.
the sum of the first 4 positive integers is less than 18 thus 1 is the smallest number; unless there is more to this question...
I saw another problem similar to this on another brain teaser site. Thankfully, given the stipulations of this one, I think I might just have it cracked:
One solution is simple:
1,2,3,4
1. Four different positive integers.
2. Sum is less than 18.
3. By knowing the product is 24 AND the least of the four integers is 1, you know the other three numbers must be 2, 3, & 4.
Then again,
2,3,5,7
1. Four different positive integers.
2. Sum is less than 18.
3. By knowing the product is 210 AND the least of the four integers is 2, you know the other three numbers must be 3, 5, & 7.
So my answer to today's brain teaser is: No, given the detail of the stipulations in the question, one cannot deduce what the set of integers is, as I have come up with two.
"To find out the four numbers you need to know their product and the smallest number"
Wrong.
1,2,4,10 total < 18
smallest = 1
product = 80
1,2,5,8 total < 18
smallest = 1
product = 80
When you say I know nothing I take offense until I realized the that I do know the product and the lowest positive interger, which also happen to be one and the same. Zero!
0+8+6+4=18
0*8*6*4=0
lowest =0
Now I am glad I know nothing.
I guess I still know nothing!
Less than eighteen? In that case make it 0+2+4+6=12 (Less than eighteen).
0*2*4*6=0
Lowest =0
Probably still wrong!
- 0(zero) is not a positive #
- 4 is a product of 2
- 6 is a product of 2 & 3
- if you pick 1, then you can't pick any other number,
because they are product of 1.
if that is true then would this be right
2+3+5+7=17 which is less than 18
none of the numbers are a product of any of the other numbers
1, 2, 4, 8
1*2=2
2*2=4
4*2=8
1+2+4+8=15
product=64
Would this not be correct?
The smallest number must be 2. As we have already seen, if the smallest number is 1, and you know the product of the four numbers, you still don't have enough information to determine, uniquely, the four numbers. This is because there are several combinations of three positive integers (assuming 1 has already been selected as the fourth), which total less than 18 and have the same product.
If the smallest number is 2, there are only 7 possible combinations, all of which, have unique products.
numbers products
2345 120
2456 200
2356 180
2346 144
2347 168
2348 192
2357 210
Because the smallest number cannot be 3 or higher (due to the fact that no combination would be less than 18), the smallest number MUST BE 2. Hence, if the product is known, so are all four of the numbers.
You all are reading into it to much. It does not say the numbers cannot be products of each other at all. In that case, I agree that there are many answers. It has been shown in the past that the poster of these indeed posts problems that have many many solutions. Sometimes these things are just not very well thought out.
ANSWER
---------------------------
Numbers are: 2, 3, 4, 5
There are 38 combinations of 4 unique digits whose sum is < 18.
The puzzle states that to know the 4 digits you would need to know their product. So, we can throw out any combination whose product is unique
(because if we are told that product we don't need to know the smallest digit).
Also, the puzzle indicates that knowing the product AND the smallest digit will allow us to identify the solution. So, a group of combinations must
have the same product AND different smallest numbers.
The only group of possible combinations that fit is:
1, 3, 5, 8 -> 120
1, 4, 5, 6 -> 120
2, 3, 4, 5 -> 120
If we are told the smallest number is 1, that isn't enough to determine the solution. So...
2, 3, 4, 5 -> 120 is the ONLY SOLUTION
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