Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 278 · 40 questions

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

1. 1.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 17 (b) 16 (c) 18 (d) 6
3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 14 (b) 13 (c) 3 (d) 15
4. 4.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
5. 5.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
6. 6.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 42 (c) 13 (d) 117
7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 14 (b) 15 (c) 13 (d) 3
8. 8.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 480 (c) 613 (d) 603
9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 4 (b) 16 (c) 15 (d) 14
10. 10.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 45? (a) 4 (b) 3 (c) 5 (d) 2
12. 12.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 24 (c) 72 (d) 75
13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 5 (b) 4 (c) 3 (d) 2
14. 14.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 283 (c) 282 (d) 260
15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 17 (b) 19 (c) 7 (d) 18
16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 19 (d) 21
17. 17.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 51 (c) 144 (d) 16
18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 18 (b) 16 (c) 19 (d) 9
19. 19.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 400 (c) 399 (d) 338
20. 20.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 21 (c) 7 (d) 24
21. 21.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 370 (c) 369 (d) 360
22. 22.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 19 (b) 8 (c) 18 (d) 17
24. 24.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 189 (c) 21 (d) 63
25. 25.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 45 (c) 15 (d) 5
26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 69? (a) 16 (b) 18 (c) 6 (d) 17
27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 1 (b) 2 (c) 4 (d) 3
28. 28.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 8 (c) 24 (d) 72
29. 29.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 36 (c) 108 (d) 12
30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 19 (b) 17 (c) 18 (d) 8
31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 11 (b) 9 (c) 13 (d) 14
32. 32.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 54 (c) 6 (d) 18
33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 19 (b) 9 (c) 20 (d) 21
34. 34.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 394 (c) 384 (d) 393
35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 5 (b) 3 (c) 4 (d) 2
36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 16 (b) 15 (c) 14 (d) 4
37. 37.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 153 (c) 54 (d) 17
38. 38.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 384 (c) 375 (d) 385
39. 39.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
40. 40.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 198 (b) 69 (c) 66 (d) 22

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