[Guest]

The Sales Manager’s Problem

The sales manager was preparing a report, and wished to include the weekly sales of the company’s best selling product, the ‘accumatic’. A colleague walked by his office, and found him perplexed. “What’s wrong”, he asked. “Well”, said the sales manager, “I seem to have lost the piece of paper with the actual number of units sold written on it. All I have is the total number of ‘accumatics’, ‘puralyzers’ and ‘macrolators’ sold scribbled in the corner of my notebook”. “That’s a problem”, said the colleague, “but what’s that other number crossed out just above it”. “Oh’, said the manager”, I added the number up with a calculator, and mistakenly used the multiplication key first time”. “Hmm, 2450, so that’s the product of the sales of all three”, said the colleague, “so you should be able to work out the number of ‘accumatics’ sold”.

His colleague came by a little later and enquired how the manager was doing. “There simply isn’t enough information here”, said the manager. “I realized that”, said the colleague”, but now I remember one of the salesmen complaining that the ‘puralyzer’ sold the least last week”. “Now I have enough information”, said the manager, “thanks a lot”.

How many ‘accumatics’ were sold?

[Jiminy Cricket]

This reminds me of a similiar riddle where two friends reunite after many years and one friend determines the ages of the other's children using the address where they used to play chess and "the youngest one likes pickles."

good riddle.

35 Accumatics were sold.

Edited January 15, 2009 by Jiminy Cricket

[Guest]

I am totally stumped! DUH!!!!!!!!!!!!!!!!!!!!!!!!!!

[Guest]

gets me totally....its as if unless you tell us the sum i can see n number of solutions from 5 to 70 (well manager knew the sum..didnt he?, so should we)

any one got any hints or anything??

Edited January 16, 2009 by DeepS

[Guest]

2450 = 2 x 5 x 5 x 7 x 7

so there are many possibilities here.

But if you said the puralyzer is the least, I assume it will be the 'very' least hence should be 2.

And accumatic is the best selling products hence should the most maximum, which should be 49

left macrolator = 25

so accumatic sales was 49.

Not very sure, could be wrong.

[Guest]

I think that without the sum there are pretty much an infinite number of answers, but here is a possible one

245

because 245 (number of best selling product)*5(middle selling product)*2(number of lowest selling product)=2450

<_<

Edited January 16, 2009 by zippzom

[Guest]

2450 = 2 x 5 x 5 x 7 x 7

so there are many possibilities here.

But if you said the puralyzer is the least, I assume it will be the 'very' least hence should be 2.

And accumatic is the best selling products hence should the most maximum, which should be 49

left macrolator = 25

so accumatic sales was 49.

Not very sure, could be wrong.

if you think least then why not 1 :-)

2450 = 1 x 2 x 5 x 5 x 7 x 7

and max is 1225.

So accumatic 1225, and macrolaro 2, puralyzer 1.

I know this can not be correct :-) the mngr could have easily remembered these figures and would not need calci to add ..

[Guest]

This reminds me of a similiar riddle where two friends reunite after many years and one friend determines the ages of the other's children using the address where they used to play chess and "the youngest one likes pickles."

good riddle.

35 Accumatics were sold.

i think the answer shud be 49.below is alist of all the possible combinations for a product of 2450.

#1 #2 #3 sum #of times this sum appears

1 1 2450 2452 1

1 2 1225 1228 1

1 5 490 496 1

1 7 350 358 1

1 10 245 256 1

1 14 175 190 1

1 25 98 124 1

1 35 70 106 1

1 49 50 100 1

2 5 245 252 1

2 7 175 184 1

2 25 49 76 1

2 35 35 72 1

5 5 98 108 1

5 7 70 82 1

5 10 49 64 2

5 14 35 54 1

7 7 50 64 2

7 10 35 52 1

7 14 25 46 1

with these combinations, there is no need for the third hint that puralyzer were sold least unless the sum that the manager knows is 64. However, if the sum is 64, only then he will have a confusion since there are 2 cases with that.

Now we can rule out 7,7,50 because then puralyzer cant be least. So the only other combination is 5, 10, 49. Since puralyzer were sold the least, their number will be 5. and since accumatic is the best selling product as indicated in the OP, its number should be 49.

[Prof. Templeton]

Just went through the trouble of writing out factors, only to be beat to the punch.

Edit: Ah, here they are anyway. Deleting would be a waste.

1 5 490 496
1 7 350 358
1 10 245 256
1 14 175 190
1 25 98 124
1 35 70 106
1 49 50 100
1 1 2450 2452
2 25 49 76
2 35 35 72
2 7 175 184
5 14 35 54
5 10 49 64
5 5 98 108
5 7 70 82
7 14 25 46
7 10 35 52
7 7 50 64

1	2	1225		1228

Edited January 16, 2009 by Prof. Templeton

[Guest]

You got it right! The key piece of information is that the puzzle is unsolvable without the final piece of information. There were 49 'accumatics' sold.

i think the answer shud be 49.below is alist of all the possible combinations for a product of 2450.

#1 #2 #3 sum #of times this sum appears

1 1 2450 2452 1

1 2 1225 1228 1

1 5 490 496 1

1 7 350 358 1

1 10 245 256 1

1 14 175 190 1

1 25 98 124 1

1 35 70 106 1

1 49 50 100 1

2 5 245 252 1

2 7 175 184 1

2 25 49 76 1

2 35 35 72 1

5 5 98 108 1

5 7 70 82 1

5 10 49 64 2

5 14 35 54 1

7 7 50 64 2

7 10 35 52 1

7 14 25 46 1

with these combinations, there is no need for the third hint that puralyzer were sold least unless the sum that the manager knows is 64. However, if the sum is 64, only then he will have a confusion since there are 2 cases with that.

Now we can rule out 7,7,50 because then puralyzer cant be least. So the only other combination is 5, 10, 49. Since puralyzer were sold the least, their number will be 5. and since accumatic is the best selling product as indicated in the OP, its number should be 49.

[Guest]

Assuming the sales manger wrote the items down as stated, accumatics, puralyzers, and macrolators in that order. Then the sales manager multiplied the first two items and added the third item. Also taking into consideration the other two numbers need to be higher the the puralycer the answer is 60 accumatics, 40 puralyzers and 50 macrolators.

I think that without the sum there are pretty much an infinite number of answers, but here is a possible one

245

because 245 (number of best selling product)*5(middle selling product)*2(number of lowest selling product)=2450

<_<