mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

More doubling cribbage

Source: Inspired by Math Puzzle of the Week blog
Brendan and Adam are playing lots more games of high stakes cribbage: whoever loses each game must double the other players money. For example, if Brendan has £3 and Adam has £4 then Brendan wins, they will have £6 and £1 respectively.
In each game, the player who has the least money wins.
Brendan and Adam notice that for some amounts of starting money, the games end with one player having all the money; but for other amounts, the games continue forever.
For which amounts of starting money will the games end with one player having all the money?

Show answer & extension

Doubling cribbage

Brendan and Adam are playing high stakes cribbage: whoever loses each game must double the other players money. For example, if Brendan has £3 and Adam has £4 then Brendan wins, they will have £6 and £1 respectively.
Adam wins the first game then loses the second game. They then notice that they each have £180. How much did each player start with?

Show answer & extension

The taxman

In a very strange country, the tax system works as follows.
£1, £2, £3 up to £12 are available.
You pick an amount. You keep this amount, but the taxman takes any factors of it. You cannot pick any amount without a factor.
This continues until you can take no more money. The taxman gets any remaining money.
For example, you might play as follows:
In this example, you end with £22 and the taxman ends with £56.
Is it possible to get more money than the taxman? What is the most you can get?

Show answer & extension

Tags: numbers, money

No change

"Give me change for a dollar, please," said the customer.
"I'm sorry," said the cashier, "but I can't do it with the coins I have. In fact, I can't change a half dollar, quarter, dime or nickel."
"Do you have any coins at all?" asked the customer.
"Oh yes," said the cashier, "I have $1.15 in coins."
Which coins are in the cash register?
(The available coins are 50¢, 25¢, 10¢ 5¢ and 1¢.)

Show answer & extension

Tags: money

Exact change

In the UK, the coins less than £1 are 1p, 2p, 5p, 10p, 20p and 50p. How many coins would I need to carry in my pocket so that I could make any value from 1p to 99p?
In the US, the coins less than $1 are 1¢, 5¢, 10¢, 25¢. How many coins would I need to carry in my pocket so that I could make any value from 1¢ to 99¢?

Show answer & extension

Tags: money, numbers

Pocket money

When Dad gave out the pocket money, Amy received twice as much as her first brother, three times as much as the second, four times as much as the third and five times as much as the last brother. Peter complained that he had received 30p less than Tom.
Use this information to find all the possible amounts of money that Amy could have received.

Show answer & extension

Tags: numbers, money

Ninety nine

In a 'ninety nine' shop, all items cost a number of pounds and 99 pence. Susanna spent £65.76. How many items did she buy?

Show answer & extension

Tags: numbers, money

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

complex numbers circles irreducible numbers trigonometry books balancing factorials hexagons menace cryptic clues determinants decahedra colouring advent bases range sets planes palindromes digital products consecutive integers mean quadratics coins cards 2d shapes integration binary fractions algebra digits albgebra polygons graphs 3d shapes division means prime numbers rectangles games doubling axes coordinates people maths expansions dice sequences perimeter median crossnumber gerrymandering crosswords logic christmas tangents integers star numbers pentagons grids parabolas dominos geometric means wordplay cubics lines digital clocks scales addition shape proportion combinatorics sums even numbers numbers ellipses chocolate probability ave spheres crossnumbers dodecagons geometric mean tournaments clocks tiling odd numbers regular shapes floors surds geometry the only crossnumber symmetry folding tube maps remainders differentiation arrows percentages cryptic crossnumbers routes unit fractions rugby sport triangle numbers matrices area calculus chess functions time indices taxicab geometry elections square numbers products cube numbers polynomials probabilty money partitions factors consecutive numbers multiplication triangles quadrilaterals pascal's triangle angles sum to infinity volume squares shapes multiples perfect numbers dates square roots chalkdust crossnumber averages speed number

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024