Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 290 · 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 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 421 (b) 352 (c) 420 (d) 411
2. 2.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) 17 (b) 54 (c) 153 (d) 51
3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 84? (a) 20 (b) 19 (c) 8 (d) 18
4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 3 (b) 4 (c) 2 (d) 5
5. 5.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 200 (b) 193 (c) 192 (d) 183
6. 6.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 15 (c) 45 (d) 48
7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 4 (b) 3 (c) 2 (d) 5
8. 8.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 373 (b) 320 (c) 372 (d) 363
9. 9.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) 6 (c) 54 (d) 18
10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 5 (b) 3 (c) 4 (d) 2
11. 11.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
12. 12.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 172 (c) 181 (d) 182
13. 13.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) 22 (b) 69 (c) 66 (d) 198
14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 93? (a) 20 (b) 18 (c) 9 (d) 19
15. 15.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 621 (c) 622 (d) 486
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) 45 (b) 5 (c) 15 (d) 18
17. 17.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 167 (c) 168 (d) 176
18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 4 (b) 3 (c) 1 (d) 2
19. 19.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
20. 20.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 330 (c) 298 (d) 339
21. 21.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 428 (b) 534 (c) 535 (d) 525
22. 22.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 4 (b) 1 (c) 3 (d) 2
24. 24.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
25. 25.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) 16 (b) 48 (c) 51 (d) 144
26. 26.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 71? (a) 6 (b) 8 (c) 5 (d) 7
28. 28.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
29. 29.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 14 (b) 3 (c) 13 (d) 15
31. 31.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
32. 32.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 213 (c) 204 (d) 214
33. 33.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
34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 18 (b) 16 (c) 6 (d) 17
35. 35.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) 36 (c) 108 (d) 39
36. 36.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) 375 (c) 384 (d) 385
37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 14 (b) 3 (c) 13 (d) 15
38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 12 (b) 11 (c) 9 (d) 8
39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 14 (b) 13 (c) 3 (d) 15
40. 40.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 254 (b) 274 (c) 273 (d) 264

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