Schools in Scotland 2022: summary statistics.
Myschool results archive#
The 20 editions are available on the archive of the Scottish Government's website. Also includes statistics from the biennial attendance, absence and exclusions collection. Statistics bulletin reporting on the annual pupil, teacher and early learning and childcare provision censuses. If your school is interested please get in touch.Summary Statistics for Schools in Scotland I give school talks about maths and puzzles (online and in person). If you would like to suggest one, email me. I’m always on the look-out for great puzzles. I set a puzzle here every two weeks on a Monday. During term time, the school posts a weekly maths challenge for curious 13-16-year olds, from which today’s puzzle was taken.
Each block in turn is transformed into the desired letter in the target word, and finally all extraneous blocks are removed completely. For example, if you want to create SILVER from nothing, double three times to get a total of 8 blocks.
Myschool results series#
Note also that this series of transformations can be applied to any block in a word, wherever it appears.īefore transforming blocks into letters, use rule 5 repeatedly to double the word, to get at least as many blocks as there are letters in the target word. Note there are two copies of each of A, U, B, Z in the block, otherwise we wouldn’t be able to transform a block into an E, O, C or Y as we wouldn’t be able to remove the single vowel or consonant trapped on one side of our desired letter. > BBCDFGHJKLMNPQRSTVWXYZZ (rule 3 – note that it says you can remove two or more vowels. For example, starting with such a block, you can get to the letter P as follows:
By using rules 3 and 4 to eliminate the unnecessary letters, it is possible to transform a block into any letter you like, or remove it entirely. We will call this sequence of letters one “block”. Start by using rules 1 and 2 repeatedly to create the following word: Now we have a form like the one in the first scenario, which we know reduces to nothing.Ĭ) Yes, you can create any word from nothing. Use rule 5 followed by rules 3 and 4 to get to the empty word.įor the final scenario, the using rule 2 to add a consonant at the end, and then delete it using rule 4. The third scenario is much the same as the first. You are left with a string of the form we had in the previous scenario, which we can transform to the empty word as above. In the second scenario, the use rule 1 to add a vowel to the front of the word. In the first scenario, use rule 5 to double the word, then use rules 3 and 4 to delete the letters in pairs starting from the middle, until you get to the empty word. Having carried out the step above, you will be left with a word of one of the following forms: Since the exact letters won’t matter for the next part of the answer, we will use the letter O to represent any vowel, and the letter X to represent any consonant. Otherwise, the remaining word must alternate between vowels and consonants. If we have reached the empty word, then we are done. We know this process must terminate because the word gets shorter at each step. You can repeat this process until there are no consecutive vowels or consonants. To start with, you can remove any consecutive vowels or consonants using rules 3 and 4. (b) Yes, all words can disappear to nothing. LEAD -> LD (rule 3) -> OLD (rule 1) -> OLDG (rule 2) -> OLDGOLDG (rule 5) -> OGOLDG (rule 4) -> OOGOLDG (rule 1) -> GOLDG (rule 3) -> GOLDGG (rule 2) -> GOLD (rule 4) (c) Can you create any word from nothing, that is, starting with the empty word can you create any target word using only the rules above? Prove the claim, or disprove it.Ī) Here’s one way. (b) Can all words disappear to nothing, that is, starting with any word, it is always possible to apply the above rules in such a way that you will get to the empty word? Prove the claim, or disprove it. (a) Starting with LEAD, find a way to make GOLD The “empty word” is a word with no letters, which we call “nothing”. Note that any string of letters is considered a word. STRING –> SING, RING, ING or STRI.ĭouble the entire word. PLEASE –>PLSE.ĭelete two or more consecutive consonants. CARD –> CARDS.ĭelete two or more consecutive vowels. MAZE –>AMAZE.Īdd any consonant to the end of a word. The following rules transform one word to anotherĪdd any vowel to the start of a word.
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