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Irish Times Maths Week Ireland 2014 Quiz

Solutions

Solutions Available Lunchtime Friday 17th October 2014

cryptarithm

The Irish Times is a great supporter of Maths Week. We can express this in a cryptarithm as

.           IRISH

+          TIMES

=          MATHS

In a cryptarithm the numbers in a sum are replaced by letters. Each letter represents a distinct digit, multiple occurrences of a letter refer to the same digit and the leftmost numbers cannot be zero. The challenge is to figure out what numbers the letters correspond to. Cryptarithms can take a lot of time and patience; they are usually solved by applying some logic and a lot of trial and error. To reduce the time demand I can tell you that R = 8 and E = 1

Budget Leaks

Amid all the budget leaks I discovered that my garden tap was leaking. Concerned about water conservation I went to repair it straight away. But, before I did I took a measuring jug from the kitchen and placed it under the offending tap. It took 1 minute 36 seconds to fill to the 1 litre mark. I wondered how much this might have cost me per year if it wasn’t discovered assuming that it was charged at Irish Water’s rate of €2.44 per cubic metre.

Six-Times Tables

There are 6 teams in the Republic of Ireland’s qualifying group for Euro 2016. Firstly, how many ways mathematically speaking, could the order of the group turn out? And, secondly if as expected, Germany tops the group and Gibraltar ends up bottom how many different ways could the group finish?

Four Digits

There are several 4-digit numbers that end with 5. But with one such number by taking the 5 from the end and putting it at the start of the number gives a number 1.2 times larger. What is the original number?

Stock Keeping

The inspector asked Farmer McCoy how much stock he had and he coyly answered:

"I have three times as many pigs as goats which are a quarter the number of cows which are half my stock."

The inspector retorted "That's not enough information for me to work it out"

"Alright", replied McCoy. "If I sell a goat and a pig and a cow next market day and buy a bull then I will have four times as many pigs as goats".

How many pigs, goats and cows does Farmer McCoy now have?

Boxing Clever

I asked a friend for measurements of the water tank he installed to collect rainwater to economise on his water charges. He reported back to me that the base was 1m2 (metre squared), the front and back were each 0.75m2 and the sides were each 0.48m2. “That’s not what I meant”, I protested. “I wanted the volume, but never mind I can work it out!” Can you figure out the volume of the tank?

Barmy Bakers

With Hallowe’en approaching a shopkeeper asked his local baker to prepare traditional barmbracks for his customers. The baker was unfamiliar with the customs so the shopkeeper explained about putting in a ring as an omen of marriage, a coin predicting wealth and a pea portending hard times. When they were delivered it transpired that the baker had put only one item in each brack. The shopkeeper was less than happy, exclaiming, “you would have to eat 15 bracks to be certain of getting a ring, you would have to eat 11 bracks to be certain of getting a coin and you would have to eat 17 to be sure of getting a pea.” How many bracks were delivered?