# Sunday Times Teaser 2985 – What’s My (Land) Line?

### by Angela Newing

#### Published December 8 2019 (link)

My telephone has the usual keypad:

1  2  3
4  5  6

7  8  9
0  0

My telephone number starts with 01 and ends in 0. All digits from 2 to 9 are used exactly once in between, and each pair of adjacent digits in the phone number appear in a different row and column of the keypad array.

The 4th and 5th digits are consecutive as are the 9th and 10th and the 8th digit is higher than the 9th.

What is my number?

The wording is loose and fails to rule out numbers with 0s & 1s “in between”.
I have found 2 such numbers. I think there may be more (even when sequences of multiple “01”s are excluded).
How much adjustment to the program would be needed to find the complete set?

Hi Tony,

If we allow consecutive repeats of the sequence ’01’ or ’10’ there are an infinite number of solutions but not allowing such repetitions gives 148,767 solutions starting and ending:

1 01867295340
2 0104351867290
3 0106729534810
4 0106751834290
5 0107629534810
6 0107681534290
7 0151034867290
8 0151043867290
9 0151072943860
10 0151076834290
……
148758 0191015101810162701030104010
148759 0191015101810162701040103010
148760 0191018101510160103010427010
148761 0191018101510160103010724010
148762 0191018101510160104270103010
148763 0191018101510160107240103010
148764 0191018101510162401030107010
148765 0191018101510162401070103010
148766 0191018101510162701030104010
148767 0191018101510162701040103010