# New Scientist Enigma 498 – Vowel Count

#### From Issue #1650, 4th February 1989

#### Vowel Count

*by Susan Denham*

In this Enigma (from “vowel” above to “?” at the end) if you put in the right numbers (in words) in the spaces then there will be … a’s, …e’s, … i’s, … o’s and … u’s.

After the correct things are put in all the spaces, how many vowels will there be (“vowel” — very end “?” inclusive)?

# New Scientist Enigma 511 – Double, Double

*by Susan Denham*

#### From Issue 1663, 6th May 1989

I wrote an odd number on the board and asked the class how many numbers (including the original number itself) could be made by writing exactly the same digits but in different orders. For example, if the number had been 5051, the answer would have been nine, namely 5051, 5015, 5105, 5150, 5501,5510, 1055, 505 and 1550). Clever Dick got the right answer immediately, so to keep him busy I told him to repeat the exercise with exactly double my original number.

“That just doubles the number of ways, Miss,” he reported. I told him to double again and repeat the exercise, and again he reported “that doubles the number of ways get again, Miss.”

So I told him to double the number yet again and to repeat the exercise with the four-figure answer. “It’s doubled the number of ways again, Miss,” he replied and, as always, he was quite right.

What number did l write on the board?

# New Scientist Enigma 516 – The ABC of Division

*by Eric Emmet*

#### From Issue 1668, 10th June 1989

In the following division sum each letter stands for a different digit. Rewrite the sum with the letter replaced by digits

# Sunday Times Teaser 2953 – Marble Tower

*by Andrew Skidmore*

#### Published April 28 2019 (link)

Liam has a number of bags of marbles; each bag contains the same number (more than 1) of equal-size marbles.

He is building a tetrahedron with the marbles, starting with a layer which fits snugly in a snooker triangle. Each subsequent triangular layer has one fewer marble along each edge. With just one bag left he had completed a whole number of layers; the number of marbles along the edge of the triangle in the last completed layer was equal to the number of completed layers. The last bag had enough marbles to just complete the next layer.

How many bags of marbles did Liam have?

# New Scientist Enigma 508 – A Colourful Deception

*by Keith Austin*

#### From Issue 1660, 15th April 1989

**Tour the Tulip Fields of Bulbania**

The towns are Aldingsp , Beachhol, Chholbea, Dingspal, Eachholb, Fresh and Gspaldin. The colours (Blue Red, Yellow) are those of the tulips in that area. You will fly to Eachholb and then drive by coach, visiting each town exactly once.

“Miss Wheel, I understand you will be driving the coach for the tour. I am afraid we have a problem. The flight is being diverted to Chholbea, so you w ill collect your passengers there.

We do not want the tourists to realise there has been a change to the tour as advertised on the above leaflet, as they might ask for their money back. Now, they will not be able to read the names of the towns as they are in Bulbattian, but they can tell the colours of tulips and they have the map. I want you to start at Chholbea and drive round visiting each town exactly once, but so that as the tourists notice the colours on each side of the road, they will believe from their map that they are following a route as described on the leaflet, beginning at Eachholb.”

What route did Miss Wheel take and what route did the tourists think they were taking?

# New Scientist Enigma Number 505 – A Pretty Puzzle

*by Christophe Maslanka*

#### Published in Issue 1657, 25th March 1989

I was just sitting down to crumpets and honey in The Wykeham Tea Room when Bob Cowley appeared carrying a basketball. He handed me a slip of paper. “**A**, **B** & **C** all stand consistently for digits throughout this equation. I won’t tell you whether any of the digits are the same or not as l don’t want to spoil your fun,” said Bob.

Certainly, it was a pretty equation:

(**BAABC** x **BA**) – **BAABC** = **ABCABC**

though l had once seen a prettier one in an amusement arcade in Bognor Regis. It should, of course, be as easy as **ABC** to solve this before the crumpets cool. Can you help me by sending me the digits corresponding to **A**, **B** and **C**?

# New Scientist Enigma 494 – Look Blank

*by Susan Denham*

#### From Issue 1646, 7th January 1989

In the following long division sum I’ve marked the position of each digit. I can tell you that there were no 1s and no 0s but that all other digits occurred at least twice.

Also (although you don’t actually need this information) all four digits of the answer were different.

What is the six-figure dividend?

# New Scientist Enigma 501 – A Reciprocal Arrangement

*by Christophe Maslanke*

#### Published in Issue 653, 25th February 1989

“As you insist on disturbing my peace of mind with puzzles.” remarked Potter to Kugelbaum as they sat down to drinks at the Maths Club. “It is only fair that you submit to the same fate.” Kugelbaum agreed. “The Egyptians expressed fractions as sums of reciprocals.” continued Potter. “For example, they wrote 3/8 = 1/8 + 1/4. That and the notion of getting one over you inspires this puzzle.”

“The smallest integer, U such that 1/U may be expressed as the sum of exactly two reciprocals in exactly and only two distinct ways is 2: 1/2 = 1/4 + 1/4 and 1/2 = 1/3 + 1/6 and there are no other ways of doing it. The second smallest is 3, since 1/3 may be expressed as the sum of exactly two reciprocals in exactly and only two distinct ways: 1/3 = 1/6 + 1/6 and 1/3 = 1/4 + 1/12. Again there are no other ways. But the third smallest value of U is not 4, since 1/4 may be expressed as the sum of two reciprocals in three distinct ways.”

“Yes.” said Kugeibaum in reply. “namely 1/8 + 1/8 + 1/12, 1/6 + 1/12 and 1/5 + 1/20. What is your question”

Potter drew himself up: “What is the eighth smallest value of U. such that 1/U is expressible as the sum of exactly and only two reciprocals in exactly and only eight distinct ways?”

Kugelbaum’s eyes glazed over and the cogs began to whir. In fact, Potter didn’t even know if the question had an answer and so when Kugelbaum gave the answer, he had to take it on trust. Given that Kugelbaum is never wrong, what was his answer?

# Sunday Times Teaser 2952 – Silly Slip

### by Victor Bryant

#### Published April 21 2019 (link)

Please help me find my silly slip. I correctly added a five-figure number to a four-figure number to give a six-figure total. Then I tried to substitute letters for digits systematically and I ended up with

**SILLY** + **SLIP** = **PLEASE**

However, in these letters I have made one silly slip, so please find it and then work out what the correct sum was.

What was the correct six-figure numerical answer?

# New Scientist Enigma 497 – The Longest Puzzle in the World?

*by Keith Austin*

#### Published in issue 1649, 28th January 1989

Hannah, Joan and Sarah each live at a different one of the three houses numbered l, 2, 3. Alan, Michael and Peter each painted a different one of those three houses. Each of the three women met a different one of the three men at the shops.

There are four clues as to who lives where and so on. However, as the clues are very long they are given here only in a condensed form, and so you may wish first to write them out in full, as indicated:

(1) Write out “the man who painted the house of the woman who met, at the shops,” (1988 + the number of the house of the woman met by Peter) times. Write the copies of the repeated phrase one after the other, and then, in from of the first copy, write “Alan is” and, after the last copy, write “Alan.” to make one very long sentence which is the first clue.

(2) This is similar to clue (1), but has “Michael is” at the start and “Peter.” at the end.

(3) Write out “the woman who met, at the shops, the man who painted the house of” (1066 + the number of the house painted by the man who met Hannah) times. Add “Hannah is” at the start and “Joan.” at the end.

(4) This is similar to clue (3) but the repeated phrase is “the house that was painted by the man who met, at the shops, the woman who lives at”. The clue starts with “Number 1 is” and ends with “Number 2.”

What are the facts, that is, who lives where, who painted which house, who met who?