**From The Sunday Times, 3rd September 1978** [link]

An electrician living in a block of flats has played a joke on the tenants by rewiring the lift. The buttons numbered 0 to 9 in the lift should correspond to the ground floor, first floor, etc., but he has rewired them so that although (for his own convenience) the buttons for the ground floor and his own floor work correctly, no other button takes you to its correct floor. Indeed when you get in the lift on the ground floor and go up, three of the buttons take you twice as high as they should, and two buttons take you only half as high as they should.

The milkman is unaware of the rewiring and so early yesterday morning, rather bleary-eyed, he followed his usual ritual which consists of taking nine pints of milk into the lift, pushing button 9, leaving one pint of milk when the lift stops, pushing button 8, leaving one pint of milk when the lift stops, and so on in decreasing order until, having pushed button and having left his last pint, he usually returns to his van.

However, yesterday when he tried to follow this procedure all seemed to go well until, having pushed button 1 , when the lift stopped he found a pint of milk already there. So he took the remaining pint back to his van, with the result that just one of the tenants (who lived on one of the floors below the electrician’s) did not get the pint of milk she’d expected.

The surprising thing was that during the milkman’s ups and downs yesterday he at no time travelled right past the floor which he thought at that time he was heading towards.

List the floors which received milk, in the order in which the milkman visited them.

This puzzle was included in the book **The Sunday Times Book of Brain-Teasers: Book 1** (1980, edited by Victor Bryant and Ronald Postill). The puzzle text above is taken from the book.

[teaser891]

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## Jim Randell 4:49 pm

on4 November 2022 Permalink |This Python program runs in 61ms. (Internal runtime is 9.2ms).

Run:[ @replit ]Solution:The ages are: 19, 31, 29, 16, 25, 23, 28, 27.With squares in square brackets:

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## Paul Byrne 9:54 pm

on14 November 2022 Permalink |Hi Jim

Thanks for all the good work on these Teasers.

Love the simplicity of your website and your solutions.

Re 3137 Teaser

Is 24 instead of 31 also a correct answer? Keep up the good work!

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## Jim Randell 9:17 am

on15 November 2022 Permalink |@Paul: Thanks for the feedback.

We can’t swap CARY for 24 in the solution I give above, as 24² = 576, and CARY and JAMES share the letter A, so their squares need to share a digit. But 576 and 841 (= 29²) don’t have any digits in common.

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## Paul Byrne 10:21 am

on16 November 2022 Permalink |Hi Jim, thank you very much for your response.

Forgive me I should’ve made myself clearer.

If Cary becomes 576, and James 784, and Steve 841, can it then work as an alternative?

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## Jim Randell 12:14 pm

on16 November 2022 Permalink |@Paul: My program performs an exhaustive search, so there is only one solution to the puzzle.

If we had:

Then {LUCY, NICK, RICKY} must correspond to {16 [256], 23 [529], 25 [625]} in some order.

LUCY is the youngest, so we have:

But then ALAN has to have digits in common with CARY [576], LUCY [256], JAMES [784], but not STEVE [841]

Which means for ALAN we need to find a square with a 7 and a 5 or a 6. The only candidate is 24 [576], but that is already used by CARY, so it is not possible to find a value for ALAN in this scenario.

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## Paul Byrne 5:17 pm

on16 November 2022 Permalink |Hi Jim

Alas I’m thwarted!

Thanks for this and all your efforts.

They are all appreciated.

Regards Paul

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