# Sunday Times Teaser 2517 – No Title

*by Andrew Skidmore*

Published December 19 2010 (link)

Finley is excited about Christmas. At school, he has made a card showing a triangular-shaped Christmas tree with a fairy on top. With this in mind, please decipher **XMAS** + **TREE** = **FAIRY**, where different letters stand consistently for different digits, and where **TREE** is a triangular number (ie, is the sum of some consecutive integers from 1 upwards).

What number is **XMAS**?

# Sunday Times Teaser 2516 – No Title

*by Nick MacKinnon*

#### Published December 12 2010 (link)

Six teams — Ayes, Bees, Cees, Dees, Ease and Fees — played each other once in a football league, with three points for a win and one for a draw. Ayes finished top, with the order of the teams being alphabetical. The difference in points between each pair of adjacent teams was the same. The 13 goals scored included hat-tricks from the Dees striker in two matches. In one game, the Cees goalkeeper let in two before being substituted.

What were Cees’ five results (in the order CvA, CvB, CvD, CvE, CvF)?

# Sunday Times Teaser 2515 – No Title

*by Des MacHale*

#### Published December 5 2010 (link)

Using each digit just once I wrote down two five-figure numbers. One was a cube and the other was a square. Then I combined these two five-figure numbers to give me a ten-figure number by using one of them to occupy the odd positions (from left to right) and the other to occupy the even positions (again from left to right). Then the four-figure number made up in order from the digits in the prime positions turned out to be prime.

What was the ten-figure number?

# Sunday Times Teaser 2514 – No Title

*by Des MacHale*

Published November 28 2010 (link)

The Hardy Annular is an ornamental garden consisting of the area between two circles with the same centre, with the radius of each a whole number of metres. A line joining two points on the circumference of the bigger circle just touches the smaller circle and measures exactly 20 metres.

What is the radius of each of the circles?

# Sunday Times Teaser 2513 – No Title

*by H Bradley and C Higgins*

#### Published November 21 2010 (link)

At the golf ball factory 10,000 balls are stored in a stack for some weeks to harden. The stack has several layers, the top layer being a single row of balls. The second layer has two rows, each with one ball more than the top row. The third layer has three rows each with two balls more than the top row, and so on.

Of the several shapes of stack possible, the one used takes up the smallest floor area.

How many balls are on the bottom layer?

# Sunday Times Teaser 2512 – No Title

*by Graham Smithers*

#### Published November 14 2010 (link)

Using each of the digits 0 to 9 exactly once, I have written down two three-figure numbers and a four- figure number.

In no particular order, one of them is a perfect square, one is a perfect cube, and the other is a prime.

If I told you which of the square, the cube and the prime was the smallest then it would be possible for you to work out what those three numbers are.

What are they?

# Sunday Times Teaser 2511 – No Title

*by Danny Roth*

#### Published November 7 2010 (link)

I have a collection of silver medallions, each of which weighs an exact whole number of grams. If I take pairs of them in every possible combination, I can weigh out an almost complete sequence of 16 consecutive weights, with only two weights, 100 grams and 101 grams, missing from the sequence. Even so, I can still manage an unbroken sequence of 13 weights, with only one of them, a prime number of grams, duplicated.

What, in ascending order, are the weights in grams of my medallions?

# Sunday Times Teaser 2510 – No Title

*by Danny Roth*

#### Published October 31 2010 (link)

Since we last met them, George has moved departments yet again and Martha has forgotten the extension number.

“No problem,” said the operator.

“If you write down the number itself, the average of its four digits, the sum of its four digits, and the cube root of the difference between the number and its reverse (which is smaller), then you will write no digit more than once.”

What is George’s new extension number?

# Sunday Times Teaser 2509 – No Title

*by Andrew Skidmore*

#### Published October 24 2010 (link)

I won £10 on the lotto with three correct numbers (in the range 1 to 49).

I then calculated the difference between two six-figure numbers: one formed by writing my three winning numbers in descending order; the other by writing them in ascending order. I multiplied this difference by three and divided the answer by the sum of my winning numbers. I then divided the new answer by one of my winning numbers. The answer was another of my three winning numbers.

What, in ascending order, were my three winning numbers?

# Sunday Times Teaser 2508 – No Title

*by Graham Smithers*

#### Published October 17 2010 (link)

An Austin pootles along a country lane at 30mph; behind are a Bentley doing 40 and a Cortina doing 50. The Bentley and the Cortina brake simultaneously, decelerating at constant rates, while the Austin carries on at the same speed. The Bentley just avoids hitting the rear of the Austin; the Cortina just avoids a collision with the Bentley. The Bentley and the Cortina continue to decelerate at the same rates, and stop with a 45yd gap between them.

What was the gap between the Bentley and the Cortina at the moment they started to brake?