## Brainteaser 1747: Lottery charges

From The Sunday Times, 10th March 1996 [link]

Chargealot are having a new set of lottery balls made. They are going to be painted with numbers from 1 (not 01) to 49. The painter decides that this is one chance to make a fortune from the lottery and so he charges accordingly. He divides the digits into two types and charges a certain whole number of pounds for painting each digit of one type (each time it occurs) and a different whole number of pounds for all the other digits (each time they occur). Both charges are more than £50 but less than £100.

To make the cost sound reasonable, instead of quoting a price for the whole set he quoted the average price per ball. Of course some balls cost less than average, and some balls cost more, but just one ball’s price was equal to the average.

What were his two charges per digit?

This puzzle was included in the book Brainteasers (2002, edited by Victor Bryant). The puzzle text above is taken from the book.

[teaser1747]