Brainteaser 1734: Scratchcard

From The Sunday Times, 10th December 1995 [link]

Every Saturday The Daily Broadsheet gives readers a free scratchcard comprising two crosses and a number of ticks concealed beneath silver foil squares. Readers have to scratch just three of the squares to reveal what is beneath. Anyone who scratches only ticks can use the card to obtain a 50p discount on The Sunday Broadsheet. The probability of revealing three ticks, expressed as a percentage, is a whole number larger than 50%.

To increase circulation the paper intends to increase the number of silver squares, still with only two crosses. This will increase the chances of finding ticks when scratching three squares, and again the probability will be a whole number percentage.

How many more silver squares do they intend to add?

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

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