Enigmatic Code

Programming Enigma Puzzles

Enigma 529: Statistical sickness

From New Scientist #1681, 9th September 1989 [link]

Only eight of our statistics students have handed in sick-leave certificates this year — which, if averaged over all our complement, would amount to precisely one day’s illness per student.

All absences were of different lengths, of between 1 and 365 days duration, with none having two consecutive digits the same, and none ending in a zero. An odd coincidence was that these eight absences were such that they split into four pairs, each member of a pair being the same as its companion with the digits reversed. But what is really strange is that these four pairs shared a further interesting property. The square of each absence was also the digit-reversal of the square of its companion.

How many students did we have this year?

[enigma529]

Enigma 523: Ivory eyewash

From New Scientist #1675, 29th July 1989 [link]

Professor Phoney O’Seven was showing Dr Dimwits a trick with numbers. He wrote 91 and 11 on the Senior Common Room white board and invited Dimwits to write down any three-digit number. Dimwits wrote down 532. Phoney explained that to find 91 × 532, he would calculate 532532 ÷ 11, which would give the required answer of 48412. This process would work whatever number Dimwits chose.

Phoney then wrote a nine-digit number and a shorter number on the board and invited Dimwits also to write down a nine-digit number. Phoney showed him how to find the product of the two nine-digit numbers quickly. He told Dimwits to write down the number consisting of Dimwits’s number written twice. Then Phoney divided it by the shorter number he had written on the board; his answer was the required product.

What was Phoney’s nine-digit number?

[enigma523]

Enigma 510: Out of court

From New Scientist #1662, 29th April 1989 [link]

Professor Puzzleothers has privately decided to allow his ex-wife a resettlement of precisely one third his current annual salary, but only if she can work out exactly how much she is to get.

He instructs his solicitor to tell her lawyers that he will agree to alimony calculated according to the following formula.

She has to find two numbers A and B which between them contain each of the digits from 1 to 9 exactly once and contain no 0 digit, such that B = 2A, A is divisible by 3, and the quotient when A is divided by 3 is a number which contains all the digits from 1 to 4. Then £A will be the annual settlement.

What does Puzzleothers currently earn?

[enigma510]

Enigma 490: Uglification practice

From New Scientist #1641, 3rd December 1988 [link]

Alice has met Professor Pip Palindrome — through the looking glass, of course. He never attempts anything which does not involve palindromes, that is, numbers which read the same from left to right as from right to left, for example 2882 or 31413.

They multiply two non-square three-digit palindromes and get an odd five-digit palindrome product, when Pip spots that this is also the product of a four-digit palindrome and a two-digit palindrome.

What was the five-digit product?

[enigma490]