## Weekly Maths Challenge

### Seven Day Maths

Challenge 213: Sequence Sums

This problem is about finite sequences where all the terms are positive integers.

One such sequence is 3, 1, 1, 2. The sequence sum for this series is 7, because

3 + 1 + 1 + 2 = 7.

How many of this kind of sequence have sequence sum 3? Or of 4? Or 5? Or 6?

Can you generalise to say how many of this kind of sequence have sequence sum n, if n is a positive integer? Explain your reasoning carefully.

There will be new Weekly Maths Challenges in the Autumn Term. Have a great summer!

Mathematics is a subject where you learn best by tackling problems. Every week, a new problem will be posted here for you to pit your wits against.

We invite you to have a go at solving it. If you get stuck, keep trying, and do go away and come back later – you will often find that you have a better idea on your second, third or even fourth attempt. If you have solved the problem, you can send your solutions to weeklymaths@kcl.ac.uk. You are welcome to either scan in written work, or to type your solutions. If you are emailing for the first time, please let us know what year you are currently in and what school you are at.

Past problems can be accessed below, and we welcome submissions of solutions for those too.

Follow us on Twitter here: @sevendaymaths, so that you never miss a new problem being posted!

Good luck!

#### Past Challenges

Weekly Challenge 212

Weekly Challenge 211

Weekly Challenge 210

Weekly Challenge 209

Weekly Challenge 208

Weekly Challenge 207

Weekly Challenge 206

Weekly Challenge 205

Weekly Challenge 204

Weekly Challenge 203

Weekly Challenge 202

Weekly Challenge 201

Weekly Challenge 200

Weekly Challenge 199

Weekly Challenge 198

Weekly Challenge 197

Weekly Challenge 196

Weekly Challenge 195

Weekly Challenge 194

Weekly Challenge 193

Weekly Challenge 192

Weekly Challenge 191

Weekly Challenge 190

Weekly Challenge 189

Weekly Challenge 188

Weekly Challenge 187

Weekly Challenge 186

Weekly Challenge 185

Weekly Challenge 184

Weekly Challenge 183

Weekly Challenge 182

Weekly Challenge 181

Weekly Challenge 180

Weekly Challenge 179

Weekly Challenge 178

Weekly Challenge 177

Weekly Challenge 176

Weekly Challenge 175

Weekly Challenge 174

Weekly Challenge 173

Weekly Challenge 172

Weekly Challenge 171

Weekly Challenge 170

Weekly Challenge 169

Weekly Challenge 168

Weekly Challenge 167

Weekly Challenge 166

Weekly Challenge 165

Weekly Challenge 164

Weekly Challenge 163

Weekly Challenge 162

Weekly Challenge 161

Problems 141-160

Problems 121-140

Problems 101-120

Problems 81-100

Problems 61-80

Problems 41-60

Problems 21-40

Problems 1-20