# Enigmatic Code

Programming Enigma Puzzles

## Enigma 976: This happy breed

From New Scientist #2131, 25th April 1998 [link]

At the end of 1991 the Society for the Protection of Our Obscure Furry Friends (SPOOFF) released a trial number of breeding pairs (born in March of that year) of the spotted tree-rat Sciurus maculatus incastus in the small forested island of Yorkiddin.

The result is a doubtful success. In 1997 they found that the island was being overrun: the local foresters were seeking compensation for damage and local rare species of birds were near extinction.

Tree-rats are born in March, and are driven from the patch of forest of their birth at the end of that year. They find a new patch, always of 2500 square metres, and immediately start breeding. They die in the fourth December of their lives. The society realised too late that every year each pair invariably produces 2 pairs of young, each of which incestuously produces 2 more pairs next year. In 1998 the number of pairs will reach nearly 6000.

The process will continue until the population reaches its limit at the beginning of 2000, when the whole forested area will have been partitioned into occupied territories.

What is the forested area in hectares? (One hectare is equal to 10,000 square metres).

[enigma976]

## Enigma 990: Sums on credit

From New Scientist #2145, 1st August 1998 [link]

The first number of the four four-digit numbers on Harry’s credit card is a prime; the second is a perfect square; the third is the sum of the first two, and is prime; and the fourth equals the third plus half the second. He has noticed that if he divides the first number by the second, and adds the result to the first, he gets the same answer as by dividing the first by the second and multiplying the result by the first.

What is the fourth number?

[enigma990]

## Enigma 1014: Mirror image

From New Scientist #2170, 23rd January 1999 [link]

Harry was playing about with his calculator and keyed in a 4-digit number. He placed a mirror behind and parallel to the display, and added the reflected number, which was smaller, to the number on the display. This gave him a 5-digit sum.

He then again keyed in the original number, and this time subtracted the reflection from it.

He divided the sum by the difference and found that the quotient was a 4-digit prime.

What was his original number?

[enigma1014]

## Enigma 1026: Dualities

From New Scientist #2182, 17th April 1999 [link] Across:

1. A prime which is also a square reversed. The first two digits form a square, and the last two a prime. The 1st, 3rd and 5th digits are all the same.
4. The square root of 7 across.
5. A palindromic square.
6. The square root of the reverse of 2 down.
7. A square which is prime when reversed.

Down:

1. A prime which is also a square reversed. The first three digits form a square which is also a square when reversed. The last two digits form a prime which is also a prime when reversed.
2. A prime which is also a square when reversed. All the digits are different. The first three digits form a square which is also a square when reversed: and the last digit is the same as that of 1 down.
3. A square which is a prime when reversed.

Find the answers for 1 across, 1 down, 3 down and 7 across.

[enigma1026]

## Enigma 1055: Solitary square

From New Scientist #2211, 6th November 1999 [link] The array above contains nine different digits. All three horizontal rows and two of the columns (reading downwards) represent 3-digit prime numbers. The other column is a perfect square. There are no leading zeros.

Find the three rows.

[enigma1055]

## Enigma 1093: Primed to spend

From New Scientist #2249, 29th July 2000 [link]

Bill’s credit card has the usual four four-digit numbers, which are in ascending order of size. All are prime numbers and the sum of the digits of each is the same.

The digits in the first number are all different and the third number is the first number reversed. The digits in the second number are all different and the fourth number is the second number reversed. The last digits of the four numbers are all different.

He has a hopeless memory for figures, but he can always work out his four-digit PIN from his card, because he can remember that it is equal to the difference between the first and third numbers (or the difference between the second and fourth numbers, which is the same) and happens to be a perfect square.

What is the fourth number?

[enigma1093]

## Enigma 1128: Daffodils

From New Scientist #2284, 31st March 2001 [link]

Saul Tregenza is a market gardener. He has a field in which he decided that it could be profitable to plant equal rows of daffodils. On a whim prompted by helping with his daughter’s homework, he decided that the number of rows and the number of bulbs in each row should be prime, and that all the digits that would form the two numbers and their product would be different.

Luckily, he found that the field is long enough to hold the maximum possible number of plants under these whimsical conditions.

What was the maximum possible number of bulbs he could plant?

[enigma1128]

## Enigma 1142: Policies with strings

From New Scientist #2298, 7th July 2001 [link]

Harry used to work for Smallprint, Wriggle, and Payless, a large insurance company. He recalls that every policy number (including some with leading “0”s) had the same number of digits, which was fewer than 20.

He also recalls being passed a neat list of the numbers of five policies for review, and being astonished to find that each number below the first on the list had exactly twice the value of the one above it, and could be obtained from the number above it merely by moving the last digit of that number to its front.

What was the bottom number on his list of five numbers?

[enigma1142]

## Enigma 1180: Anomalies

From New Scientist #2336, 30th March 2002 [link]

SEVEN is a prime, and as one would expect, SEVEN minus THREE equals FOUR. But perversely, FOUR is a prime, (and is also a prime when the digits are in reverse order), so THREE is not a prime. Another anomaly is that TEN is a perfect square.

Each different capital letter above represents a different digit, which is the same for that letter everywhere.

Find the numerical values of FOUR and TEN.

[enigma1180]