## Brainteaser 1771: Lottery logic

**From The Sunday Times, 25th August 1996** [link]

For his weekly flutter on the National Lottery my friend has to select six of the numbers between 1 and 49 inclusive. Last week he wrote his numbers in numerical order and noticed something which he thought would interest me.

The first three numbers written in succession, with no gaps, formed a perfect square. The remaining three, similarly combined, formed another square. He suggested I try to deduce his six numbers.

Fortunately I knew his largest number was even and that he always chose one single-digit number.

Which numbers had he selected?

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

[teaser1771]

## Jim Randell 1:58 pm

on15 December 2019 Permalink |This Python program runs in 74ms.

Run:[ @repl.it ]Solution:The numbers chosen are: 2, 13, 16, 21, 34, 44.We have: 21316 = 146², 213444 = 462².

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## GeoffR 10:21 am

on16 December 2019 Permalink |LikeLike

## John Crabtree 4:39 pm

on18 December 2019 Permalink |The second square must end in 44 (sq. root = 362 + 50x or 338 + 50x), 36 (sq. root = 344 + 50x or 356 + 50x), or 24 (sq. root = 332 + 50x or 318 + 50x). By use of a calculator, the second square = 213444

Then the first square must end in 16 (sq. root = 104 + 50x or 146 + 50x). Again by use of a calculator, the first square = 21316.

And so the six numbers are 2, 13, 16, 21, 34 and 44.

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