Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 310 · 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.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 57 (c) 60 (d) 19
2. 2.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 405 (c) 396 (d) 406
3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 19 (b) 20 (c) 18 (d) 8
4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 17 (b) 8 (c) 18 (d) 19
5. 5.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 352 (c) 421 (d) 420
6. 6.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 116 (c) 125 (d) 134
7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 15 (b) 13 (c) 4 (d) 14
8. 8.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) 13 (c) 42 (d) 117
9. 9.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) 72 (b) 69 (c) 207 (d) 23
10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 8 (b) 9 (c) 6 (d) 7
11. 11.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 472 (c) 386 (d) 471
12. 12.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 159 (b) 168 (c) 150 (d) 160
13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 5 (b) 4 (c) 6 (d) 3
14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 4 (b) 5 (c) 2 (d) 3
15. 15.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) 24 (b) 7 (c) 63 (d) 21
16. 16.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) 5 (b) 45 (c) 15 (d) 18
17. 17.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
18. 18.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 90 (c) 98 (d) 80
19. 19.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) 72 (b) 27 (c) 24 (d) 8
20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 14 (b) 4 (c) 15 (d) 16
21. 21.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 8 (b) 19 (c) 18 (d) 20
23. 23.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 4 (b) 14 (c) 15 (d) 13
25. 25.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 313 (b) 303 (c) 280 (d) 312
26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 2 (b) 1 (c) 3 (d) 4
27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 16 (b) 14 (c) 4 (d) 15
28. 28.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 367 (b) 316 (c) 357 (d) 366
29. 29.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 151 (c) 152 (d) 160
30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 17 (d) 16
31. 31.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 496 (c) 637 (d) 636
32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 7 (b) 17 (c) 18 (d) 19
33. 33.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
34. 34.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 306 (c) 352 (d) 351
35. 35.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 459 (c) 469 (d) 468
36. 36.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 33 (c) 11 (d) 99
37. 37.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) 10 (b) 90 (c) 33 (d) 30
38. 38.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 174 (c) 192 (d) 184
39. 39.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 312 (c) 286 (d) 322
40. 40.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) 81 (b) 9 (c) 30 (d) 27

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