Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 114 · 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 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) 54 (b) 153 (c) 17 (d) 51
2. 2.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 261 (c) 246 (d) 252
3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 18 (b) 17 (c) 7 (d) 19
4. 4.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) 18 (b) 57 (c) 54 (d) 162
5. 5.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 404 (c) 489 (d) 499
6. 6.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) 72 (b) 216 (c) 24 (d) 75
7. 7.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 16 (b) 14 (c) 6 (d) 15
9. 9.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
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 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) 207 (b) 72 (c) 69 (d) 23
12. 12.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 270 (c) 279 (d) 258
13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 17 (b) 15 (c) 5 (d) 16
14. 14.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
15. 15.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) 11 (b) 99 (c) 36 (d) 33
16. 16.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 250 (c) 268 (d) 258
17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 2 (b) 3 (c) 5 (d) 4
18. 18.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) 36 (b) 108 (c) 39 (d) 12
19. 19.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 131 (c) 132 (d) 140
20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 16 (b) 14 (c) 4 (d) 15
21. 21.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) 48 (b) 45 (c) 135 (d) 15
22. 22.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) 30 (c) 81 (d) 27
23. 23.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 346 (c) 302 (d) 345
24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 1 (d) 4
25. 25.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 17 (b) 6 (c) 16 (d) 18
27. 27.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) 24 (c) 21 (d) 7
28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 3 (b) 4 (c) 2 (d) 5
29. 29.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 326 (b) 372 (c) 381 (d) 382
30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 15 (b) 4 (c) 14 (d) 16
31. 31.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 414 (c) 354 (d) 424
32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 13 (b) 4 (c) 14 (d) 15
33. 33.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) 30 (b) 90 (c) 10 (d) 33
34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 17 (b) 15 (c) 16 (d) 7
35. 35.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
36. 36.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) 19 (d) 60
37. 37.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 429 (c) 439 (d) 364
38. 38.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) 13 (b) 117 (c) 42 (d) 39
39. 39.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 356 (b) 427 (c) 417 (d) 426
40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 3 (b) 6 (c) 5 (d) 4

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