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Christmas card 2019
2019-12-08
Just like last year, the year before and the year before, TD and I spent some time in November this year designing a Chalkdust puzzle Christmas card.
![](javascript:showlimage("card2019.jpg"))
The card looks boring at first glance, but contains 9 puzzles. By splitting the answers into two digit numbers, then drawing lines labelled with each number (eg if an answer is 201304, draw the lines labelled 20, 13 and 4), you will reveal a Christmas themed picture. Colouring the regions of the card containing circles red, the regions containing squares green, and the regions containing stars white or yellow 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 two digit numbers, the lines will be drawn, and the regions will be coloured...
| 1. | If you write out the numbers from 1 to 10,000 (inclusive), how many times will you write the digit 1? | Answer |
| 2. | What is the sum of all the odd numbers between 0 and 86? | Answer |
| 3. | How many numbers between 1 and 4,008,004 (inclusive) have an odd number of factors (including 1 and the number itself)? | Answer |
| 4. | In a book with pages numbered from 1 to 130,404, what do the two page numbers on the centre spread add up to? | Answer |
| 5. | What is the area of the largest area quadrilateral that will fit inside a circle with area 60,153π? | Answer |
| 6. | There are 5 ways to write 4 as the sum of ones and twos (1+1+1+1, 1+1+2, 1+2+1, 2+1+1, and 2+2). How many ways can you write 28 as the sum of ones and twos? | Answer |
| 7. | What is the lowest common multiple of 1025 and 835? | Answer |
| 8. | How many zeros does 245! (245!=245×244×243×...×1) end in? | Answer |
| 9. | Carol picked a 6-digit number then removed one of its digits to make a 5-digit number. The sum of her 6-digit and 5-digit numbers is 334877. Which 6-digit number did she pick? | Answer |
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Comments
Comments in green were written by me. Comments in blue were not written by me.
2019-12-17
Rishabh, what do you see that I do not?Rob Glencairn
Thanks for the feedback. (I now understand the need for redaction). My son sent me your link as a Xmas present. I must think of an appropriate retaliation. (What is a PDF?)Think I've fixed 1,6 and 9....8 eludes me, for the moment.
Rob
@Rob: It looks to me like you've made mistakes in questions 1, 6, 8, and 9. The hints from the back of the pdf might help:
1. How many numbers between 1 and 10,000 have 1 as their final digit? How many have 1 as their penultimate digit?
6. How many ways can you write 1? 2? 3? 4? 5? What's the pattern?
8. How many zeros does 10! end in? How many zeros does 20! end in? How many zeros does 30! end in?
9. Carol’s sum is odd. What does this tell you about the 5- and 6-digit numbers?×1 ×1 ×2 ×1 ×2
1. How many numbers between 1 and 10,000 have 1 as their final digit? How many have 1 as their penultimate digit?
6. How many ways can you write 1? 2? 3? 4? 5? What's the pattern?
8. How many zeros does 10! end in? How many zeros does 20! end in? How many zeros does 30! end in?
9. Carol’s sum is odd. What does this tell you about the 5- and 6-digit numbers?
Matthew
×1 ×1 ×2 ×1 ×2 I'm 71, with one good eye left. What am I missing?
1. 400001
2. 1849
3. 2002
4. 130405
5. 120306
6. 53?
7. 171175
8. 59?
9. 313525
1. 400001
2. 1849
3. 2002
4. 130405
5. 120306
6. 53?
7. 171175
8. 59?
9. 313525
Rob
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