## Brainteaser 1734: Scratchcard

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

Every Saturday

The Daily Broadsheetgives 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 onThe 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.

[teaser1734]

## Jim Randell 9:39 am

on17 October 2019 Permalink |If there are

nticks (wheren ≥ 3), then the probability of scratching off 3 ticks is:This Python program finds values of

nwhere this probability is an integer percentage, greater than 50%.Run:[ @repl.it ]Solution:They intend to add 9 more squares.With 16 squares (14 ticks and 2 crosses) the probability is 65%.

With 25 squares (23 ticks and 2 crosses) the probability is 77%.

In fact there are only 4 values for

nwhich give an integer percentage forp:LikeLike