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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 750 · 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.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) 18 (c) 5 (d) 15
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 19 (b) 18 (c) 9 (d) 20
  3. 3.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 140 (c) 150 (d) 149
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 5 (b) 7 (c) 4 (d) 6
  5. 5.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 343 (b) 333 (c) 342 (d) 300
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 77? (a) 5 (b) 6 (c) 7 (d) 8
  7. 7.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 211 (b) 212 (c) 210 (d) 201
  8. 8.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 230 (c) 237 (d) 238
  9. 9.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 483 (c) 474 (d) 484
  10. 10.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 391 (b) 332 (c) 381 (d) 390
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 5 (b) 6 (c) 3 (d) 4
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 5 (d) 4
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 14 (b) 13 (c) 3 (d) 15
  14. 14.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) 198 (c) 66 (d) 69
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 13 (b) 15 (c) 3 (d) 14
  16. 16.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) 19 (c) 60 (d) 57
  17. 17.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 6 (b) 4 (c) 3 (d) 5
  19. 19.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 540 (c) 550 (d) 549
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  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) 45 (b) 135 (c) 15 (d) 48
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 3 (b) 6 (c) 4 (d) 5
  23. 23.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 52? (a) 3 (b) 6 (c) 5 (d) 4
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 73? (a) 7 (b) 5 (c) 8 (d) 6
  26. 26.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) 489 (c) 480 (d) 490
  27. 27.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) 69 (b) 72 (c) 23 (d) 207
  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 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 190 (c) 198 (d) 189
  30. 30.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 271 (b) 252 (c) 261 (d) 270
  31. 31.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) 180 (b) 60 (c) 63 (d) 20
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 4 (b) 16 (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) 33 (c) 10 (d) 90
  34. 34.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 11 (d) 8
  35. 35.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 588 (c) 598 (d) 470
  36. 36.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 450 (c) 372 (d) 451
  37. 37.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 278 (b) 300 (c) 309 (d) 310
  38. 38.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
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 20 (b) 21 (c) 9 (d) 19
  40. 40.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) 16 (c) 48 (d) 144

Answer key

  1. 15
  2. 19
  3. 149
  4. 6
  5. 342
  6. 7
  7. 210
  8. 237
  9. 483
  10. 390
  11. 5
  12. 5
  13. 14
  14. 66
  15. 14
  16. 57
  17. 2
  18. 5
  19. 549
  20. 4
  21. 45
  22. 5
  23. 6
  24. 5
  25. 7
  26. 489
  27. 69
  28. 27
  29. 189
  30. 270
  31. 60
  32. 15
  33. 30
  34. 9
  35. 597
  36. 450
  37. 309
  38. 372
  39. 20
  40. 48

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