Maths Puzzles


The following puzzles are from the Transum monthly newsletters and podcasts.

Exam Average

What mark is required in the last exam to achieve an 80% overall average?

Cake Cut

Where should the last slice of cake be cut to give two equal pieces?

Holy Sphere

Calculate the remaining volume of the sphere after a cylindrical hole has been drilled through the centre

Jumping Flea

How many different places could the flea find itself after 8 foot-long jumps either north, south, east or west?

Last Digit

How many positive two-digit numbers are there whose square and cube both end in the same digit?

Central Station

The probability that the next train to leave will be going north is five times the probability that the next train to leave will be going south.

Canteen Queue

Is it possible to answer the question if Betsy's age is not known?

Separated Twins

Work out the combination of the safe given the clues about pairs of numbers.

Divisible By Three

A puzzle about two digit numbers that can be made from ten different digits.

Letters In Numbers

A brand new puzzle involving the letters in numbers when written as words.

Square Angled Triangle

The angles of a triangle are all square numbers. What are they?

Tri-Junction Puzzle

What is the probability of the three cars arriving at the road junction not being involved in an accident?

Two Prime Squares

What is the smallest square number (greater than one) that cannot be expressed as the sum of two prime numbers?

The Missing Pound

Where did the missing pound go in this story about three people visiting a restaurant?

Ticks, Tocks, Tacks and Tucks

Find how ticks compare to tocks, tacks and tucks from the given information.

The Power of Christmas

A question about indices to get you thinking mathematically at this festive time of year.

Ant and Dec

What single question could Dec ask Ant to find out what he is thinking?

Bookworm

How far does the bookworm travel on its meal-time journey?

Three Mathematicians

How can the third mathematician be so certain that everyone wants a drink?

Unfinished Game

If the coin tossing game was cut short how would you share the winnings?

Alphanumbetical

Questions about the letters used to make the natural numbers.

Best Dice

Which of the unusual dice would you choose to give you the best chance of winning the prize?

The Birthday Problem

What is the probability of two or more pupils in a class having the same birthday?

Enigma Vowels

A coding question inspired by the film The Imitation Game.

Biased Coin

A mathematical question asked by Microsoft and Google interviewers.

Twelve Days of Christmas

Can you figure out exactly how many gifts the true love sends during the twelve days of the Christmas holiday?

Chased by a Bear

A puzzle about an explorer being chased by a bear along with a question about imperial and metric measures with Measurement Man

Halloween Bases

A puzzle about Why is halloween like Christmas along with news of the new Number Skills Inventory

Torch Tunnel

A puzzle about four people making their way through a tunnel with just one torch along with news of the new numerology page

Cube in Milk

A puzzle about a cube being lowered into a bucket of milk along with news of the new shunting puzzles

Eric Levy, United States

Thursday, November 17, 2016

"Thank you for the podcasts! I really enjoy the puzzles. This relates to the 5/29/15 podcast re: coin flipping game that was stopped before completion. The flips when stopped were two Heads and one Tail. You indicate that the options on next 2 tosses are HH, TH, HT, and TT. Since the game stops when one person reaches 3 points, wouldn't HH and HT be the same, as the second flip isn't needed? This seems to match your ultimate answer of 75% and 25%, though ... with the person with Tails only winning with TT, which is 25% chance. I get the same answer but intermediate steps differ. Am I looking at this incorrectly? Thanks!."

Transum,

Thursday, November 17, 2016

"Dear Eric, Thanks so much for your observations and you are completely right. The only reason I chose to list the next two outcomes was to produce equally likely outcomes making the arithmetic very slightly easier. I am glad you enjoy the puzzles."

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