## Teaser 2991: Super Street

**From The Sunday Times, 19th January 2020** [link]

George and Martha and their five daughters with their families have moved into six houses in Super Street. I define a “super prime number” as a prime number which has at least two digits adding up to a prime number (e.g. 11 and 23). Similarly for “super squares” (e.g. 36) and “super cubes”. Houses in Super Street are numbered with the lowest 31 super numbers of the above types.

The elderly couple live in the highest-numbered house on the street. They noticed that the last digits of their daughters’ houses were five consecutive digits and the sum of their five house numbers was a perfect square. Furthermore, the ordinal positions (lowest-numbered house is 1 and so on) of all but one of the houses were prime.

Which five houses did the daughters occupy?

[teaser2991]

## Jim Randell 9:43 am

on22 January 2020 Permalink |I took the definition of a “super-

p” numbernto be as follows:This seems to be the required interpretation (a possible alternative interpretation gives no solutions).

This Python program runs in 304ms.

Run:[ @repl.it ]Solution:The house numbers of the daughters are: 23, 125, 137, 144, 196.George and Martha live at house number 199 (super-prime).

The daughters live at the following house numbers:

The sum of the house numbers is 625 (= 25²).

And the units digits form the sequence: (3, 4, 5, 6, 7).

The ordinal of house number 144 is not prime, but the rest are.

If we allow single digit “super” numbers, then we get the following solution:

George and Martha live at house number 157 (super-prime).

The daughters live at the following house numbers:

The sum of the house numbers is 400 (= 20²).

And the units digits form the sequence: (0, 1, 2, 3, 4).

The ordinal of house number 100 is not prime, but the rest are.

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