### Problem Solving class

Is there enough information to solve this problem?

"The clown speaks to the magician: 'I lent some money to five people here and still haven't been paid back. You're one of them; the other four owe me twelve dollars altogether, but I don't remember how much each of them owes me separately.'

'Whole dollars, no cents?'

'Yes. I do remember that the four other debts multiplied together equals your debt. Do you remember how much you owe me?'

'Yes, but I still can't figure out how much each of the other four owe you.'

'Wait; the lion tamer is the one who owes me the least.'

'That'll do it! Now I know the amount of each debt.'

How much did each of the five people owe the clown?"

I don't see how there is enough info to have only one possible answer. I mean, it could be that the debts are 1, 2, 4, 5, and 40, or it could be that the debts are 3, 4, 4, 5, and 240. All I seem to realize that I know is that one debt is smaller than all the others, that four added together equal 12 and that the product of those same four is the fifth. I don't see how that is enough--am I wrong?

"The clown speaks to the magician: 'I lent some money to five people here and still haven't been paid back. You're one of them; the other four owe me twelve dollars altogether, but I don't remember how much each of them owes me separately.'

'Whole dollars, no cents?'

'Yes. I do remember that the four other debts multiplied together equals your debt. Do you remember how much you owe me?'

'Yes, but I still can't figure out how much each of the other four owe you.'

'Wait; the lion tamer is the one who owes me the least.'

'That'll do it! Now I know the amount of each debt.'

How much did each of the five people owe the clown?"

I don't see how there is enough info to have only one possible answer. I mean, it could be that the debts are 1, 2, 4, 5, and 40, or it could be that the debts are 3, 4, 4, 5, and 240. All I seem to realize that I know is that one debt is smaller than all the others, that four added together equal 12 and that the product of those same four is the fifth. I don't see how that is enough--am I wrong?