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Puzzles

5 December

Today's number is the number of ways that 35 can be written as the sum of distinct numbers, with none of the numbers in the sum being divisible by 9.
Clarification: By "numbers", I mean (strictly) positive integers. The sum of the same numbers in a different order is counted as the same sum: eg. 1+34 and 34+1 are not different sums. The trivial sum consisting of just the number 35 counts as a sum.

4 December

Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, 4+3×2 is 14, not 10. Today's number is the product of the digits in the red boxes.
+÷= 2
+ ÷ -
÷-= 5
÷ - ×
-×= 4
=
3
=
5
=
6
Tags: grids, numbers

3 December

What is the volume of the smallest cube inside which a rectangular-based pyramid of volume 266 will fit?

2 December

What is the maximum number of lines that can be formed by the intersection of 30 planes?

1 December

One of the digits of today's number was removed to leave a two digit number. This two digit number was added to today's number. The result was 619.

Largest odd factors

Pick a number. Call it \(n\). Write down all the numbers from \(n+1\) to \(2n\) (inclusive). For example, if you picked 7, you would write:
$$8,9,10,11,12,13,14$$
Below each number, write down its largest odd factor. Add these factors up. What is the result? Why?

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Square factorials

Source: Woody at Maths Jam
Multiply together the first 100 factorials:
$$1!\times2!\times3!\times...\times100!$$
Find a number, \(n\), such that dividing this product by \(n!\) produces a square number.

Show answer & extension

An arm and a leg

If 60% of people have lost an eye, 75% an ear, 80% an arm and 85% a leg, what is the least percentage of people that have lost all four?

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