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## Be Positive

Posted by rajesh on October 17, 2011 – 8:21 pm

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?

This post is under “Tom” and has 3 respond so far.

### 3 Responds so far- Add one»

1. 1. Wizard of Oz Said：

This one seems familiar . . .
Without working through all the possibilities it would seem that we need several combinations of numbers which have the same product, but only one of these has a unique smallest number.
The product 120 can be formed from 2345, 1456 and 1358. Only 2345 has a unique first number so I think that this is the one you want.
However, there may be other combinations with a different product that fit. I haven’t checked them all.

2. 2. Chris Said：

Writing the possibilities out as ABCD,Sum,Product, we get
1 2 3 4, 24
1 2 3 5, 30
1 2 3 6, 36
1 2 3 7, 42
1 2 3 8, 48
1 2 3 9, 54
1 2 3 10, 60
1 2 3 11, 66
1 2 4 5, 40
1 2 4 6, 48
1 2 4 7, 56
1 2 4 8, 64
1 2 4 9, 72
1 2 4 10, 80
1 2 5 6, 60
1 2 5 7, 70
1 2 5 8, 80
1 2 5 9, 90
1 2 6 7, 84
1 2 6 8, 96
1 3 4 5, 60
1 3 4 6, 72
1 3 4 7, 84
1 3 4 8, 96
1 3 4 9, 108
1 3 5 6, 90
1 3 5 7, 105
1 3 5 8, 120
1 3 6 7, 126
1 4 5 6, 120
1 4 5 7, 140
2 3 4 5, 120
2 3 4 6, 144
2 3 4 7, 168
2 3 4 8, 192
2 3 5 6, 180
2 3 5 7, 210

The question implies that it is not sufficient to to merely know that the product is unique. As we’re in puzzleland, we can immediately remove all cases with a unique product, to get:

1 2 3 10, 60
1 2 4 9, 72
1 2 4 10, 80
1 2 5 6, 60
1 2 5 8, 80
1 2 5 9, 90
1 2 6 7, 84
1 2 6 8, 96
1 3 4 5, 60
1 3 4 6, 72
1 3 4 7, 84
1 3 4 8, 96
1 3 5 6, 90
1 3 5 8, 120
1 4 5 6, 120
2 3 4 5, 120

Only 2 3 4 5 can be singled out on the basis that it’ smallest member, 2, also has to be known. Just like wot Wiz said.

3. 3. vedsar Said：

The total combinations, if the sum of all the four digits are 18 is
I will tell you later the meaning of the last number.
1 2 3 12 — 8
1 2 4 11 — 7
1 2 5 10 — 6
1 2 6 9 — 5
1 2 7 8 — 14