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## Sunday, 3 August 2014

### Sunday Afternoon Maths XXIII

Here's this week's collection. Answers & extensions tomorrow. Why not discuss the problems on Twitter using #SundayAfternoonMaths or on Reddit.

#### Let the Passenger Train Through!

A goods train, made up of a locomotive and 5 trucks, stops at a small station. The small station has a siding which the goods train can reverse into. The siding can hold an engine and two trucks or three trucks.
A passenger train arrives travelling in the opposite direction. How can they let it through? (The passenger train is too long to fit in the siding.)

#### Cooked Turkey

An old invoice showed that seventy-two turkeys had been purchased for "—67.9—". The first and last digits were illegible.
How much did one turkey cost?

#### Mrs. Coldcream Objected

"I object," said Councillor Mrs. Coldcream. "I see no reason why the boys should be so favoured at the expense of the girls."
This was at a meeting of the Holmshire Education Committee. It had been proposed to award 19 scholarships totalling £1000 to boys and girls of the county. It had been proposed that each girl receive a set amount and each boy receive £30 more than each girl.
Mrs. Coldcream pressed her point with such fervour that it was decided to reallocate the money. Each girl would receive £8 more than originally proposed, with the boys' scholarships scaled down accordingly.
How much did each boy and each girl receive?

#### Ten Digit Number

Can you create a 10-digit number, where the first digit is how many zeros in the number, the second digit is how many 1s in the number etc. until the tenth digit which is how many 9s in the number?