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Number Detective

Follow the clues to find the mystery number.

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Six Is the Sum

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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ABC

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Song Book

Age 7 to 11 Challenge Level:

A school song book contains 700 songs, numbered 1 to 700.

Each month at a special assembly, the children sing four different songs.

The numbers of the songs are displayed to the children by putting together single-digit cards like this:

 
 

The card for 6 may be turned upside down to serve as a 9.

What is the minimum number of digit cards that is needed to show any possible combination of four song numbers?

How many of each digit must there be?