# 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?

Solution 20 bracks

The baker would need to eat

15 bracks to be certain of getting a ring

11 bracks to be certain of getting a coin and

17 to be sure of getting a pea.

This means that there are

14 bracks that have no ring

10 bracks with no coin

16 bracks with no pea.

If we call the number of bracks with a ring, R

And, we call the number of bracks with a coin, C

And the number of bracks with a pea, P

Then

C + P = 14     (1)

R + P = 10     (2)

R + C = 16     (3)

R + C = 16      (3)

-  (R + P = 10)     (2)

=  C - P = 6

C-  P =  6

+(C + P) = 14

2C = 20

C = 10

R + C = 16

C = 10

Therefore

R = 6

C + P = 14

C = 10

P = 4

R + C + P  = 6 + 10 + 4 = 20