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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 566 · 40 questions
TalentJR

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.

NameDateTime takenScore ___ / 40
  1. 1.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 5 (b) 7 (c) 8 (d) 6
  2. 2.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 312 (c) 351 (d) 361
  3. 3.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) 11 (c) 99 (d) 33
  4. 4.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 82 (c) 100 (d) 91
  5. 5.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) 18 (d) 15
  6. 6.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) 7 (c) 24 (d) 21
  7. 7.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 394 (c) 384 (d) 334
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 7 (d) 9
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 6 (b) 5 (c) 4 (d) 7
  10. 10.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 271 (c) 252 (d) 261
  11. 11.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 434 (c) 543 (d) 544
  12. 12.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 265 (c) 248 (d) 264
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 77? (a) 7 (b) 6 (c) 5 (d) 8
  14. 14.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  15. 15.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  16. 16.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 65 (b) 66 (c) 56 (d) 74
  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) 51 (b) 48 (c) 16 (d) 144
  18. 18.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 147 (b) 148 (c) 156 (d) 138
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 9 (b) 19 (c) 20 (d) 21
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 6 (b) 4 (c) 3 (d) 5
  21. 21.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) 363 (c) 320 (d) 372
  22. 22.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 15 (b) 16 (c) 17 (d) 6
  24. 24.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) 24 (b) 27 (c) 72 (d) 8
  25. 25.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 399 (c) 338 (d) 390
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 9 (b) 18 (c) 20 (d) 19
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 3 (d) 4
  28. 28.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) 30 (b) 81 (c) 27 (d) 9
  29. 29.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 517 (c) 416 (d) 516
  30. 30.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 93 (b) 84 (c) 102 (d) 94
  31. 31.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  32. 32.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 567 (c) 558 (d) 568
  33. 33.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) 417 (c) 427 (d) 426
  34. 34.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) 108 (b) 12 (c) 39 (d) 36
  35. 35.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  36. 36.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 160 (c) 142 (d) 151
  37. 37.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 34 (c) 52 (d) 43
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 4 (b) 15 (c) 16 (d) 14
  39. 39.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 324 (c) 288 (d) 325
  40. 40.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 1 (d) 18

Answer key

  1. 7
  2. 360
  3. 33
  4. 91
  5. 15
  6. 21
  7. 393
  8. 8
  9. 6
  10. 270
  11. 543
  12. 264
  13. 7
  14. 4
  15. 2
  16. 65
  17. 48
  18. 147
  19. 20
  20. 5
  21. 372
  22. 3
  23. 16
  24. 24
  25. 399
  26. 19
  27. 3
  28. 27
  29. 516
  30. 93
  31. 7
  32. 567
  33. 426
  34. 36
  35. 8
  36. 151
  37. 43
  38. 15
  39. 324
  40. 2

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