Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 337 · 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.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 78 (c) 60 (d) 69
2. 2.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 398 (b) 480 (c) 489 (d) 490
3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 15 (b) 17 (c) 16 (d) 6
4. 4.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 3 (b) 2 (c) 4 (d) 1
6. 6.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 183 (c) 192 (d) 174
7. 7.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 12 (b) 11 (c) 4 (d) 10
9. 9.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 280 (c) 270 (d) 279
10. 10.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 20 (c) 180 (d) 63
11. 11.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 81 (c) 30 (d) 27
12. 12.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 117 (c) 118 (d) 126
13. 13.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
14. 14.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
15. 15.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 33 (b) 42 (c) 34 (d) 24
16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 16 (b) 17 (c) 15 (d) 5
17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 5 (b) 16 (c) 17 (d) 15
18. 18.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 23 (b) 72 (c) 207 (d) 69
19. 19.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 366 (c) 442 (d) 432
20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 3 (b) 2 (c) 4 (d) 5
21. 21.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) 63 (b) 66 (c) 189 (d) 21
22. 22.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 600 (b) 472 (c) 591 (d) 601
23. 23.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 142 (c) 151 (d) 152
24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 6 (b) 5 (c) 7 (d) 4
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) 5 (c) 15 (d) 45
26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 19 (b) 9 (c) 20 (d) 21
27. 27.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 261 (c) 252 (d) 262
28. 28.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) 18 (d) 6
29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 3 (b) 14 (c) 13 (d) 15
30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 98? (a) 19 (b) 20 (c) 9 (d) 21
31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 20 (b) 21 (c) 19 (d) 9
32. 32.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 3 (d) 10
33. 33.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) 12 (b) 39 (c) 36 (d) 108
34. 34.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 10 (c) 33 (d) 30
35. 35.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 468 (c) 390 (d) 478
36. 36.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 162 (c) 57 (d) 18
37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 16 (b) 7 (c) 18 (d) 17
38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 3 (b) 1 (c) 2 (d) 4
39. 39.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 210 (c) 211 (d) 201
40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 12 (b) 3 (c) 14 (d) 13

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