# Enigmatic Code

Programming Enigma Puzzles

## Enigma 1078: Think

From New Scientist #2234, 15th April 2000 [link]

In the two multiplications shown (where both products are identical), all the digits have been replaced by letters and asterisks. Different letters stand for different digits, but the same letter always stands for the same digit whenever it appears. An asterisk can be any digit.

How much is THINK?

[enigma1078]

## Enigma 1092: A prime age

From New Scientist #2248, 22nd July 2000 [link]

Marge, April, May, June, Julia and Augusta have all celebrated their birthday today. They are all teenagers and with the exception of the one pair of twins their ages are all different.

Today, only Marge and April have ages which are prime numbers, but the sum of the ages of all the girls is also a prime number. On their birthday last year, only May and June had ages which were prime numbers, but again the sum of the ages of all the girls was a prime number. On their birthday two years before that, only May and Julia had ages which were prime numbers, but even then, the sum of the ages of all the girls was again a prime number.

How old is Augusta?

[enigma1092]

## Enigma 1100: Sydney 2000

From New Scientist #2256, 16th September 2000 [link]

Whether it’s the “Sydney 2000 games in year 2000” or the “Games in year 2000 in Sydney”, either way, both are arranged in additions (I) and (II), where the only given digits appear in the number 2000 as shown and all other digits have been replaced by letters and asterisks.

In these additions, different letters stand for different digits and the same letter always stands for the same digit whenever it appears, while an asterisk can be any digit.

What is the numeric value of SYDNEY?

[enigma1100]

## Enigma 1113: Ten + ten = twenty

From New Scientist #2269, 16th December 2000 [link]

In the multiplications shown, where the combined products of multiplications (I) and (II) (both identical) equal the product of multiplication (III), each letter consistently represents a specific digit, different letters being used for different digits while asterisks can be any digit.

The multiplications in fact are not difficult to solve, and easier still if I told you that TEN is even.

How much is TWENTY?

[enigma1113]

## Enigma 1120: Assorted numbers

From New Scientist #2276, 3rd February 2001 [link]

Consider the five-digit and six-digit numbers represented by the words MELONS, PLUMS, APPLES, LEMONS and BANANA, in which different letters stand for different digits but the same letter always stands for the same digit whenever it appears.

If the product 2 × MELONS is greater than the product 35 × PLUMS, but less than the product 3 × APPLES; and if the product 99 × LEMONS is greater than the product 16 × APPLES, but less than the product 210 × PLUMS, then how big is a BANANA?

Thanks to Hugh Casement for providing the source for this puzzle.

[enigma1120]

## Enigma 1125: The same sum

From New Scientist #2281, 10th March 2001 [link]

As you can see, my three additions have the same sum [total] and in all additions different letters stand for different digits but the same letter always stands for the same digit whenever it appears. Asterisks can be any non-zero digit.

If THIS and THAT are both even, what is the sum of any addition?

[enigma1125]

## Enigma 1133: Smile

From New Scientist #2289, 5th May 2001 [link]

In the given multiplication (which contains no zeros), different letters stand for different digits but the same letter always stands for the same digit and a smiley face of course, can be any digit.

If YES is odd, how big is your SMILE?

[enigma1133]

## Enigma 1139: A simple addition

From New Scientist #2295, 16th June 2001 [link]

The simple addition, 0 + 2 + 7 + 11 = 20, may also be written as shown in the diagram where different letters stand for different digits and the same letter stands for the same digit.

What is the value of NIL?

[enigma1139]

## Enigma 1144: Isaac Newton (?-1727)

From New Scientist #2300, 21st July 2001 [link]

Isaac Newton, 1642-1727? or 1643-1727? The discrepancy of course is due to the overlap of the Julian and Gregorian calendars and to avoid any controversy I have omitted his birth year altogether in the given multiplications, leaving only 1727 as shown. All other digits have been replaced by letters and asterisks.

However, the mechanistic laws of motion attributed to this great scientists provide another clue and this is given by the simple equation: F = m × A.

In the multiplications and the clue, different capital letters stand for different digits and the same capital letter stands for the same digit. Asterisks and the lower-case letter, m, can be any digit.

What is the value of SCIENTIST?

[enigma1144]

## Enigma 1173: Six months

From New Scientist #2329, 9th February 2002 [link]

The months MAY, JUN, JUL and AUG are indicated in the two multiplications shown where all the digits have been replaced by capital letters and asterisks. In these multiplications, and in the clues that follow, different capital letters stand for different digits but the same capital letter always stands for the same digit while the asterisks can be any digit.

Typically, the months JAN and MAR are both exactly divisible by 31, and of course you can also assume that any YEAR is exactly divisible by 12 or even 52.

What is the product of each multiplication?

[enigma1173]

## Enigma 1412: Any amount

From New Scientist #2572, 7th October 2006

I have a five-digit TOTAL, a six-digit AMOUNT, and several other whole numbers, all expressed in words written in capital letters, where different letters stand for different digits and the same letter stands for the same digit.

A few curious properties are noticeable. For instance, if you add ANY amount to my TOTAL, and then divide by say, A value, the result is a whole number.

And if you subtract AN amount from my AMOUNT then divide by say, ANY value, the result, of course, is ANY amount.

How much is my five-digit VALUE?

There are now 457 Enigma puzzles up on the site – which means there are only 1300 “Classic” puzzles remaining to publish!

[enigma1412]

## Enigma 1442: Seventy-five

From New Scientist #2603, 12th May 2007

The number 75 is prominent in these three additions, where the undisclosed digits have been replaced by letters and question marks. Different letters represent different digits, and the same letter consistently represents the same digit. A question mark can be any digit, and as usual, leading digits cannot be zero. What number is LESS?

[enigma1442]

## Enigma 1462: Coloured cubes

From New Scientist #2623, 29th September 2007

In the following statements different capital letters in bold stand for different digits, with the same letter consistently standing for the same digit.

I have a collection of cubes in three different colours: red, blue and yellow. Their sides are all whole numbers, and furthermore I can tell you that the volume of each red cube is NIL, the face of each blue cube has NO area and the volume of each yellow cube is ZERO. Obviously the total volume of all the cubes is NOTHING. As for quantities, if you arrange the cubes into three distinct piles according to colour, you will find that in one pile there are NO cubes and in another pile there are NONE.

How many cubes are in the remaining pile, and what is their colour?

[enigma1462]

## Enigma 1493: A simple multiplication

From New Scientist #2655, 10th May 2008

In the multiplication shown below, the digits have been replaced by letters and asterisks. Different letters stand for different digits, the same letter stands for the same digit, an asterisk can be any digit, and leading digits cannot be zero.

What is the six-figure product?

[enigma1493]

## Enigma 1496: Eighteen

From New Scientist #2658, 31st May 2008

An eight-digit “multiplicand” comprising dots and letters is multiplied by 2 resulting in the product EIGHTEEN, as shown in the multiplication below, where different letters stand for different digits, the same letter stands for the same digit, and a dot can be any digit.

What is the eight-letter product EIGHTEEN?

[enigma1496]

## Enigma 1506: China games

From New Scientist #2668, 9th August 2008

In the three arithmetic additions below, the number 2008 is given and the undisclosed digits have been replaced by letters and smiley faces. Different letters stand for different digits (the same letter consistently stands for the same digit), each face can be any digit, and leading digits cannot be zero.

Find the value of GAMES.

[enigma1506]

## Enigma 1515: Relative sizes

From New Scientist #2677, 11th October 2008

In the following statements, whole numbers are expressed in words written in capital letters, where different letters stand for different digits, the same letter consistently stands for the same digit, and leading digits cannot be zero.

If the total of four BEES and a SNAIL is greater than the total of eight FLEAS and an ANT; and if the total of 18 ANTS and a GNAT is greater than the total of 18 FLIES and a FLEA, find the value of BEETLES.

[enigma1515]

## Enigma 1558: Mirror image

From New Scientist #2721, 15th August 2009 [link]

The digits in the two addition sums are all non-zero and have been replaced by letters and smiley faces. Different letters stand for different digits, the same letter stands for the same digit, and each emoticon can be any digit.

If the six-digit summation of either addition is a mirror image (i.e. reverse) of the other, find the value of MIRAGE.

[enigma1558]

## Enigma 1564: My favourite number

From New Scientist #2727, 26th September 2009 [link]

My favourite number consists of several digits and is not included on my list of five whole numbers (comprising non-zero digits) written below in capital letters, where different letters stand for different digits and the same letter stands for the same digit.

I can tell you that although my favourite number is smaller than the BEST number, which is twice as GOOD, and larger than the ODD prime number, there is a BETTER number that is bigger than the OTHER number, which is exactly 25 times my favourite number.

What is my favourite number?

[enigma1564]

## Enigma 1568: Odd puzzle

From New Scientist #2731, 24th October 2009 [link]

In this multiplication sum the digits have been replaced by letters and dots. Different letters stand for different digits, the same letter stands for the same digit, each dot can be any digit, and leading digits cannot be zero.

What is the six-figure odd PUZZLE?

[enigma1568]