Christmas card 2018

2018-12-08

The card looks boring at first glance, but contains 10 puzzles. By splitting the answers into pairs of digits, then drawing lines between the dots on the cover for each pair of digits (eg if an answer is 201304, draw a line from dot 20 to dot 13 and another line from dot 13 to dot 4), you will reveal a Christmas themed picture. Colouring the region of the card labelled R red or orange will make this picture even nicer.

If you want to try the card yourself, you can download this pdf . Alternatively, you can find the puzzles below and type the answers in the boxes. The answers will be automatically be split into pairs of digits, lines will be drawn between the pairs, and the red region will be coloured...

If you enjoy these puzzles, then you'll almost certainly enjoy this year's puzzle Advent calendar

1. What is the smallest four digit number whose digits add up to 6? Answer

2. What is the length of the hypotenuse of a right angled triangle whose two shorter sides have lengths 152,560 and 114,420? Answer

3. What is the lowest common multiple of 1346 and 196? Answer

4. What is the sum of all the odd numbers between 0 and 698? Answer

5. How many numbers are there between 100 and 10,000 that contain no 0, 1, 2, or 3? Answer

6. How many factors ( including 1 and the number itself ) does the number \(2^{13}\times3^{19}\times5^9\times7^{39}\) have? Answer

7. In a book with pages numbered from 1 to 16,020,308, what do the two page numbers on the centre spread add up to? Answer

8. You think of a number, then make a second number by removing one of its digits. The sum of these two numbers is 18,745,225. What was your first number? Answer

9. What is the largest number that cannot be written as \(13a+119b\), where \(a\) and \(b\) are positive integers or 0? Answer

10. You start at the point (0,0) and are allowed to move one unit up or one unit right. How many different paths can you take to get to the point (7,6)? Answer



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