The modified puzzle of Martin Gardner
A number's persistence is the number of steps required to reduce it to a single digit by multiplying all its digits to obtain a second number, then multiplying all the digits of that number to obtain a third number, and so on until a one-digit number is obtained. For example, 77 has a persistence of four because it requires four steps to reduce it to one digit: 77-49-36-18-8. The smallest number of persistence one is 10, the smallest of persistence two is 25, the smallest of persistence three is 39, and the smaller of persistence four is 77. What is the smallest number of persistence eleven?
The answer is 277777788888899.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
This is a list of the smallest numbers of persistence n with (1≤n≤11).
(1) 10
(2) 25
(3) 39
(4) 77
(5 ) 679
(6) 6788
(7) 68889
(8) 2677889
(9) 26888999
(10) 3778888999
(11) 277777788888899 ---> (answer of this problem)